There is a logically consistent world, where you made all the same observations, and coin came up tail. It may be a world with different physics than the world with coin coming up head, which means that result of coin toss is an evidence in favor of particular physical theory.
And yeah, there are no worlds with different pi.
EDIT: Or, to speak more precise, maybe there is some sorta-cosistent sorta-sane notion of the “world with different pi”, but we currently don’t know how to build it and if we knew, we would have solved logical uncertainty problem.
Meta-point: your communication pattern fits with following pattern:
The reason why smart people find themselves in this pattern is because they expect short inferential distances, i.e., they see their argumentation not like vague esoteric crackpottery, but like a set of very clear statements and fail to put themselves in shoes of people who are going to read this, and they especially fail to account for fact that readers already distrust them because they started conversation with <controversial statement>.
On object level, as stated, you are wrong. Observing heuristic failing should decrease your confidence ih heuristic. You can argue that your update should be small, due to, say, measurement errors or strong priors, but direction of update should be strictly down.