[taeric]

Apologies, was away from computer for the extended weekend.

The crux of my view on this problem is that I can make an "at least" or an "at most" statement only knowing what one of the coins is, specifically. So, we both flip a coin, I look at mine and say "at least one is heads." You do not get an increased odds of knowing your coin, obviously. (This is the general play of liar's dice. Just, with dice. :) )

That all said, I largely land on agreeing with one of the other commenters here. The assumptions you can bring to this scenario are rather large here. The assumption I would hold would be to mirror this with how it could happen "in the world." And most ways of selecting a family where "at least 1 is a girl" has you encountering a girl. That is, ordering the two events and revealing one at a time.

In modeling this, you could say that you have two coins, one marked with heads on each side and the other a standard fair coin. In this, I can easily see how your odds of seeing heads on the first coin is increased, but odds on them being both heads is now back to 1/2. I can see how this is not the same modeling you are using, but it is still one that I have a hard time shaking from my intuition on the problem.