but they're a problem precisely because our current best physical theories tell us that brains can fluctuate into existence.

Yes, but our current best physical theories also mean that they probably fluctuate into existence considerably less often than they form under normal circumstances (human brains, at least). A mind is a complex thing, so the amount of information it takes to replicate a mind is probably far higher than the amount of information it takes to specify an environment likely to give rise to a mind. If you discard the causal process that gives rise to minds in practice and postulate thermal noise as the cause instead, you end up postulating Boltzmann brains as well.

I didn't mean that Boltzmann brains are a particularly big philosophical problem, just that they become one when you try to do philosophy where you postulate very specific things occurring by "random chance".