I took it to my LBS today and they fixed it in an hour, no questions asked, and were really nice. Turns out it was a washer sitting in the portion of the brake that indicates what gear you're in. They greased it up really good and the rattling went away.

They said worst case scenario, they would contact Shimano to get a replacement (which wasn't necessary) but they weren't sure they would do anything since it was a "lower end" component -- I am learning the hard way just how expensive bikes are, I guess. I didn't think a $900 bike was "low end" but hey, whatever, it's fixed!