You could not have been anyone but what you are - namely, one specific dynamic pattern of matter and energy embedded within physics.

So imagine that post-singularity scientists find evidence of a Parallel Earth, but aren't able to measure or observe it directly. After a bunch of work, they come up with a device that can interact with the parallel world, but only in a very specific way: it connects to the mind of a single intelligent life-form there, and transmits its thoughts and sensations back to you in a sort of "virtual reality". Only problem is they don't know how to aim it: as far as anyone knows, it samples randomly across all space and time when choosing its subject. Also, they only have enough funding to use the device once.

So they aim it and they end up in the body of some guy. The tech level around him seems to be approximately medieval, and he seems to be speaking a Tocharian language. Unfortunately, just then some barbarians show up and kill him, and the device explodes.

What information can we glean about Parallel Earth from this experiment? Well, we know that at least one person spoke Tocharian there in medieval times. But it's unlikely that just one person speaks Tocharian there - if one person spoke Tocharian, and everyone else speaks (let's say) Basque, then it would be hugely improbable that the random device would have chosen the one Tocharian speaker. Because our random sampling device chose a Tocharian speaker, we have some evidence that Tocharian is probably one of the more common languages on Parallel Earth.

We can go even further. Our subject lived in medieval times, we live in post-singularity times and observe a galactic population of five hundred trillion. If Parallel Earth also experiences a singularity with a population of five hundred trillion, and we are genuinely selecting at random from everyone who ever lived, it would be extremely weird for our machine to randomly select one of the (let's say) 500 million people in ancient times as opposed to the 500 trillion people in post-singularity times: in fact, the chances are only (500 mil/500 tril) = (1/1 million). This provides Bayesian evidence that Parallel Earth humanity managed to destroy itself before reaching a singularity.

Anthropics is just the belief that just as I can draw inferences from some machine placing me a randomly selected Parallel Earthling's body, so I can draw inferences from blind luck placing me in a randomly selected Real Earthling's body.

I'm curious to know where you disagree here. Do you think the scientists shouldn't draw inferences based on their device selecting that ancient Tocharian-speaker, or do you think they are justified in their assumptions but present-day anthropic reasoners are not?