I think people get it wrong because they assume that with two options the odds are the same, and you can't know anything to make it otherwise. That's why it can help to explain about where the knowledge is.

One reason why g is close to pi^2 is related to the original idea to define the metre as being the pendulum length required to give a 1 second half-tick. If that's your definition of the metre then g is exactly pi^2. So in some sense it's not entirely coincidence. I should go and find the stack exchange discussion, but I don't have time just now.

And thank you for the compliment about my patience - I appreciate it.