But even if it is getting people to donate significantly more to organizations doing actual work, which is hard to quantify, saying that directly is saving hundreds of thousands of lives seems like a stretch to me as well. I credit those organizations, not the foundation reviewing them.
Your skepticism is fair but I think if you did a deeper dive you might come to the same conclusion that the effective altruism movement has significantly increased charitable funding to those organizations that in turn have saved many more lives than they otherwise would have.
Also, I did not calculate that number, that was a rough estimate from some other source (I don’t remember off the top of my head) but it does seem reasonable to me based on my understanding of the increased attention to global health via EA backed charities.