1. Why do you guys think that AM’s rate of finding blocks is poission distributed? It is definitely not a poisson process, but I admit that that fact does not preclude its results from being poission distributed. That being said, due to the variance in AM's hash rate that friedcat has admitted, we know that it is not poisson distributed.
Block discovery is still Poisson distributed.
According to Wikipedia: "[...] the Poisson distribution [...] is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event."
What matters is the average rate. It does not matter that the rate fluctuates.
So we do have a Poisson distribution, though we don't know the average rate exactly.
2. Many of you are missing a crucial point. The difference between the expected value for a GIVEN 6 hour period is a VERY DIFFERENT question from the probability that 0 blocks will be found in ANY ONE 6 hour period. Allow me to illustrate with an example, and I think even you condescending / smug posters will understand. The probability of flipping a coin 3 times and getting heads each time is VERY DIFFERENT from flipping a coin 50 times a getting a string of 3 heads in a row. I really hope you guys see why... Now, I know thinking is difficult but please try. Now think for an example how this concept applies to this situation. Do you see now?
Using your coin flipping analogy: Why not flip the coin 500 times? 5000? An infinite number of times? This is uninteresting. Given very long time periods we can expect any number of unlikely events (e.g. Boltzmann brains).
What we are interested in is a given 6 hour period.