Why do we often see 2 blocks mined within a few seconds of each other? This seems to happen far more frequently than one would expect from a Poisson distribution with a ~10 minute mean. Am I just bad at statistics or is something else going on?
is something else going on?


Maybe.

AFAIK Mining nodes don't synchronize time. Timestamps in blocks are not accurate. You cannot tell the elapsed time between two blocks by looking at timestamps in those blocks.