The history of effective altruism is littered with over-confident claims, many of which have later turned out to be false. In 2009, Peter Singer claimed that you could save a life for $200 (and many others repeated his claim).

I think this sentence misrepresents Peter Singer's position. Here's a relevant excerpt from The Life You Can Save (pp. 85-87, 103). As you can see, Singer actually criticizes many organizations for providing excessively optimistic estimates, and doesn't himself endorse the $200 per-life-saved figure.

For saving lives on a large scale, it is difficult to beat some of the campaigns initiated by the World Health Organization (WHO) […]

The WHO campaigns have saved lives and prevented blindness. But how efficiently have they used their resources—that is, how much have they cost per life saved? Until we can get closer to answering this question, it’s going to be hard to decide how to use our money most effectively. Organizations often put out figures suggesting that lives can be saved for very small amounts of money. WHO, for example, estimates that many of the 3 million people who die annually from diarrhea or its complications can be saved by an extraordinarily simple recipe for oral rehydration therapy: a large pinch of salt and a fistful of sugar dissolved in a jug of clean water. This lifesaving remedy can be assembled for a few cents, if only people know about it. UNICEF estimates that the hundreds of thousands of children who still die of measles each year could be saved by a vaccine costing less than $1 a dose. And Nothing But Nets, an organization conceived by American sportswriter Rick Reilly and supported by the National Basketball Association, provides anti-mosquito bed nets to protect children in Africa from malaria, which kills a million children a year. In its literature, Nothing But Nets mentions that a $10 net can save a life: “If you give $100 to Nothing But Nets, you’ve saved ten lives.”

If we could accept these figures, GiveWell’s job wouldn’t be so hard. All it would have to do to know which organization can save lives in Africa at the lowest cost would be to pick the lowest figure. But while these low figures are undoubtedly an important part of the charities’ efforts to attract donors, they are, unfortunately, not an accurate measure of the true cost of saving a life.

Take bed nets as an example. They will, if used properly, prevent people from being bitten by mosquitoes while they sleep, and therefore will reduce the risk of malaria. But not every net saves a life: Most children who receive a net would have survived without it. Jeffrey Sachs, attempting to measure the effect of nets more accurately, took this into account, and estimated that for every one hundred nets delivered, one child’s life will be saved every year (Sachs estimated that on average a net lasts five years). If that is correct, then at $10 per net delivered, $1000 will save one child a year for five years, so the cost is $200 per life saved (this doesn’t consider the prevention of dozens of debilitating but nonfatal cases). But even if we assume that these figures are correct, there is a gap in them—they give us the cost of delivering a bed net, and we know how many bed nets “in use” will save a life, but we don’t know how many of the bed nets that are delivered are actually used. And so the $200 figure is not fully reliable, and that makes it hard to measure whether providing bed nets is a better or worse use of our donations that other lifesaving measures. […]

It’s difficult to calculate how much it costs to save or transform the life of someone who is extremely poor. We need to put more resources into evaluating the effectiveness of various programs. Nevertheless, we have seen that much of the work done by charities is highly cost-effective, and we can reasonably believe that the cost of saving a life through one of these charities is somewhere between $200 and $2,000.