Why do the 3-color passport stamps have to be distributed normally? If some patterns were more common than others, than couldn't it explain the 55.55%?
The problem is that quantum mechanics predicts (and experiments show) that the distribution you actually get is 50%, which is lower than what you would expect no matter what stamp configuration you get.
On the other hand, it's possible that the way you choose which door to open is not distributed randomly. One of the ways to reconcile Bell's theorem is that there's a passport stamp that mind-controls you into picking doors with a 50% distribution. It's not a very popular theory, but it exists. [2]
[1] Assuming RGG without loss of generality
1-R 1-R = Match
1-R 2-G = Miss
1-R 3-G = Miss
2-G 1-R = Miss
2-G 2-G = Match
2-G 3-G = Match
3-G 1-R = Miss
3-G 2-G = Match
3-G 3-G = Match
Five matches to four misses.