>"vaguely P(observations|pure noise generator) ~ P(pure noise generator | observations)"

For this to be true, P(observations) ~ P(pure noise generator) as you said earlier. Anyway, you can look at it from either perspective, doesn't really matter.

On what basis do you claim this is reasonable to expect? I suspect you have none whatsoever... in fact simple thought experiments will lead us to the opposite conclusion, and there is plenty of data telling us the same.