I think this is confusing priors and posteriors.

Anthropics seems to be built around the idea of using who you are as evidence. P(humans have not blown ourselves up|I am a human) is high, so long as you accept that "I am a human" is a meaningful observation.

For the way you phrased it, "at least one human exists" would give the same answer, but imagine that not everyone would die. There being at least one human is a given.

Should that suggest that his conclusion is wrong?

There's a few distinct possibilities to consider:

• The physicist is a human, and his theory is wrong. (Moderate prior)

• The physicist is a human, and his theory is right. (Exponentially tiny prior)

• The physicist is a Boltzmann brain, and his theory is wrong. (Tiny prior)

• The physicist is a Boltzmann brain, and his theory is right. (Very tiny prior)

If he's right, he's almost certainly a Boltzmann brain, since an actual human evolving in that universe requires far too many coincidences. But if he's a Boltzmann brain, he has no reason to believe that theory, since it's based on a chance hallucinated memory rather than actual experiments, and the theory is most likely wrong. And if the theory is wrong, it would be pretty surprising to hallucinate something like humanity, so he probably is a real person.

Thus, the most likely conclusion is that his theory is wrong, and he's a human.