The main issue I am skeptical of is the statistics rather than the neuroscience. Just because the brain can be stored in 10^10 bits does not imply that measuring O(10^10) bits at random will give you what you want. But perhaps Paul has a reason to believe this beyond e.g. the intuition from the fact that random projections work for compressed sensing (which seems qualitatively different to me, since recovering L^2 distances is a much less structured problem than recovering brains, so we have more reason to believe in that scenario that random bits are approximately as good as carefully chosen bits).