Thanks for your reply.
As I mentioned, I can take screenshots just fine with 5 random games out of my library (both disc and digital games) and share/edit them as I see fit, so I'm really quite familiar with the process and quite sure it's a problem with the game itself. To test it thoroughly, I took about 30 screens through this procedure but got nothing. Other games respond directly.
I searched on this page and someone else had a similar problem with NHL (along several other people) and was told by Microsoft that they needed to adjust something in his account and it suddenly worked. Can you figure out what that mysterious tweak is? Chances are it's the same issue.
I should mention that I was able to take screenshots before the patches hit, and before I was an xbox live gold member. Ever since both events, it stopped working for this game in particular.