We're proud to say that we don't have any bootleg shirts on our site!
The way this works is that we have an agreement with the NFLPA (the NFL Players Association) - the union that represents the players in the NFL. When our team of designers comes up with a new idea for a shirt (for example, one with Peyton Manning on it), we send it over to the guys at the NFLPA who are in charge of things like this (T-shirts, bobbleheads, etc. - all sorts of merchandise). The players have authorized these guys to speak for them in matters like this, so if they think it's not too outrageous and doesn't portray Peyton Manning in a way that he wouldn't be okay with, they can OK our shirt idea without having to go and ask Peyton what he himself thinks about it.
We don't have to go through the NFL at all because as far as pictures of the players are concerned, the NFLPA holds all the cards. If we wanted to sell a shirt with (say) the Denver Broncos logo on it, that's when we'd have to get in touch with the NFL. But if we're just concerned with pictures of the players, we only need to talk with the NFLPA.