If I wanted to exterminate the human race using nanotechnology, there are two methods I would think about. First method, airborne replicators which use solar power for energy and atmospheric carbon dioxide for feedstock. Second method, nanofactories which produce large quantities of synthetic greenhouse gases. Under the first method, one should imagine a cloud of nanodust that just keeps growing until most of the CO2 is used up (at which point all plants die). Under the second method, the objective is to heat the earth until the oceans boil.
For the airborne replicator, the obvious path is "diamondoid mechanosynthesis", as described in papers by Drexler, Merkle, Freitas and others. This is the assembly of rigid nanostructures, composed mostly of carbon atoms, through precisely coordinated deposition of small reactive clusters of atoms. To assemble diamond in this way, one might want a supply of carbon chains, which remain sequestered in narrow-diameter buckytubes until they are wanted, with the buckytubes being positioned by rigid nanomechanisms, and the carbon chains being synthesized through the capture and "cracking" of CO2 much as in plants. The replicator would have a hard-vacuum interior in which the component assembly of its progeny would occur, and a sliding or telescoping mechanism allowing temporary expansion of this interior space. The replicator would therefore have at least two configurations: a contracted minimal one, and an expanded maximal one large enough to contain a new replicator assembled in the minimal configuration.
There are surely hundreds or thousands of challenging subproblems involved in the production of such a nanoscale doomsday device - power supply, environmental viability (you would want it to disperse but to remain adrift), what to do with contaminants, to say nothing of the mechanisms and their control systems - but it would be a miracle if it was literally thermodynamically impossible to make such a thing. Cells do it, and yes they are aqueous bags of floppy proteins rather than evacuated diamond mechanisms, but I would think that has more to do with the methods available to DNA-based evolution, rather than the physical impossibility of free-living rigid nanobots. The Royal Society report to which you link hardly examines this topic. It casually cites a few qualitative criticisms made by Smalley and others, and attaches some significance to a supposed change of heart by Drexler - but in fact, Drexler simply changed his emphasis, from accident to abuse. There is no reason to expect free-living rogue replicators to emerge by accident from nanofactories, because such industrial assemblers will be tailored to operate under conditions very different to the world outside the factory. But there has been no concession that free-living nanomechanical replicators are simply impossible, and people like Freitas and Merkle who continue to work on the details of mechanosynthesis have many time expressed the worry that it looks alarmingly easy (relatively speaking) to design such devices.
As for my second method, you don't even need free-living replicators, just mass production of the greenhouse-gas nanofactories, and a supply of appropriate ingredients.
I'm not sure if this counts as an existential threat, but I'm more concerned about a biowar wrecking civilization-- enough engineered human and food diseases that civilization is unsustainable.
I can't judge likelihood, but it's at least a combination of plausible human motivations and technology. Your tech is plausible, but it's hard to imagine anyone wanting not just to wipe out the human race, but also to do such damage to the biosphere.
There are a few people who'd like the human race to be gone (or at least who say they do), but as far as I know, they all want plants and animals to continue without being affected by people.
An example of the collective action failures that happen when millions of not-so-bright humans try to cooperate. From the BBC:
US President Barack Obama had laid out his vision for the future of human spaceflight. He was certain that low-Earth orbit operations should be handed to the commercial sector - the likes of SpaceX and Orbital Sciences Corp. As for Nasa, he believed it should have a much stronger R&D focus. He wanted the agency to concentrate on difficult stuff, and take its time before deciding on how America should send astronauts to distant targets such as asteroids and Mars.
This vision invited fury from many in Congress and beyond because of its likely impact in those key States where the re-moulding of the agency would lead to many job losses - in Florida, Texas, Alabama and Utah.
The continued provision of seed funding to the commercial sector to help it develop low-cost "space taxis" capable of taking astronauts to and from the ISS. The funding arrangements would change, however. Instead of the White House's original request for $3.3bn over three years, the Committee's approach would provide $1.3bn. (Obama had wanted some $6bn in total over five years; the Committee says the total may still be possible, but over a longer period)
Make-work bias and pork-barrel funding are not exactly news, but in this case they are exerting a direct negative influence on the human race's chances of survival.
Opinion in singularitarian circles has gradually shifted to under-emphasizing the importance of space colonization for the survival of the human race. The justification is that if a uFAI is built, we're all toast, and if an FAI is built, it can build spacecraft that make the Falcon 9 look like a paper aeroplane.
However, the development of any kind of AI may be preceded by a period where humanity has to survive nano- or bio-disasters, which space colonization definitely helps to mitigate. Before or soon after we develop cheap, advanced nanotechnology, we could already have a self-sustaining colony on the moon (though this would require NASA to get its ass in gear).
I leave you with an artist's impression of the physical embodiment of government inefficiency, a spacecraft optimized to make work rather than to advance the prospects of the future of the human race:
The Space Shuttle cost $1.5 billion per launch (including development costs), so with a payload of 25 tons to LEO, that makes a cost of $60,000 per kg to orbit. Falcon 9 gets 10 tons to orbit for $50 million, making a cost of $5000/kg, and falcon 9 heavy gets 32 tons for (apparently) 78 million, a price of $2500/kg. As the numbers clearly indicate, what we need is obviously another space shuttle.
How realistic is a risk-reducing colony?
Robin Hanson points out that a self-sustaining space/lunar/Martian colony is a long way away, and Vladimir Nesov and I point out that self-sustaining is unnecessary: a colony somewhere (the moon, under the ground on earth, Antarctica, etc) needs only to be able to last a long time, and be able to un-do the disaster. So Vladimir suggests a quarantined underground colony that can do Friendly AI research in case of a Nuclear/Nanotech/Biotech disaster.
Space colonies versus underground colonies
Space provides an inherent cost disadvantage to building a long-life colony that is basically proportional to the cost per kg to orbit. Once the cost to orbit falls below, say, $200/kg, the cost of building a very reliably quarantined, nuke-proof shelter on earth will catch up with the costs inherent in operating in vacuum.
It was also noted that motivating people to become lunar or Martian colonists with disaster resilience as a side benefit seems a hell of a lot easier than motivating them to be underground colonists. An underground colony with the sole aim of allowing a few thousand lucky humans to survive a major disaster is almost universally perceived negatively by the public; it pattern matches with "unfair", "elitists surviving whilst the rest of us die", etc, and it should be noted that de facto no-one constructed such a colony even though the need was great in the cold war, and no-one has constructed one since, or even tried to my knowledge (though smaller underground shelters have been constructed, they wouldn't make the difference between extinction and survival).
On the other hand, most major nations have space programs, and it is relatively easy to convince people of the virtue of colonizing mars; "The human urge to explore", etc. Competitive, idealistic and patriotic pressures seem to reinforce each other for space travel.
It is therefore not the dollar cost of a space-colony versus an underground colony, but amount of advocacy required to get people to spend the requisite amount of money that matters. It may be the case that no realistic amount of advocacy will get people to build or even permit the construction of a risk-reducing underground colony.
Rhetoric versus rational planning
The thoughts that you verbalize whilst planning risk-reduction are not necessarily the same as the words you emit in a policy debate. Suppose that there is some debate involving an existential risk-reducer (X), a space advocate (S), and a person who is moderately anti-space exploration (A) (for example, the public).
Perhaps S has A convinced to not block space exploration in part because saving the human race seems virtuous, and then X comes along and points out that underground shelters do the same job more efficiently. X has weakened S's position more than she has increased the probability of an underground shelter being built. Why? First of all, in a debate about space exploration, people will decide on the fate of space exploration only, then forget the details. The only good outcome of the debate for X is that space exploration goes ahead. Whether or not underground shelters get built will be (if X is really lucky) another debate entirely (most likely there will simply never be a debate about underground shelters)
Second, space is a rhetorically strong position. It provides jobs (voters are insane: they are pro-government-funded-jobs and anti-tax), it fulfills our far-mode need to be positive and optimistic, symbolizing growth and freedom, and it fulfills our patriotic need to be part of a "great" country. Also don't underestimate the rhetorical force of the subconscious association of "up" with "good", and "down" with "bad". Underground shelters have numerous points against them: they invoke pessimism (they're only useful in a disaster), selfishness (wanting to live whilst others die), "playing god" (who decides who gets to go in the shelter? Therefore the most ethical option is that no-one goes in the shelter, thinks the deontologist, so don't bother building it) and injustice.
So by pointing out that space is not the most efficient way to achieve a disaster-shelter, X may in fact increase existential risk. If instead she had cheered for space exploration and kept quiet about underground options or framed it as a false dichotomy, S's case would have been strengthened, and some branches of the future that would otherwise have died survive. Furthermore, it may be that X doesn't want to spend her time advocating underground shelters, because she thinks that they have worse returns that FAI research. So X's best policy is to simply mothball the underground shelter idea, and praise space exploration whenever it comes up, and focus on FAI research.