EDIT: I am not saying it has to make sense to the rest of the series either. It makes no sense that all other heroes would coincidentally wear a hat after that moment. I think the creators were of the mindset of "hey, this is supposed to be the first game of the series, let's throw in this cool thing about his hat". In other words, the two are linked. Because it's the first in the series, supposedly, they put the hat reference in. It's merely an intention for TMC to come first.