Really? You don't think they have people just trolling and looking? Or perhaps more likely, some flawed, hacked together piece of software that attempts to do it automatically, with fingerprinting, or even worse, by filename?
Fair use rules need to be expanded to work with the digital world. Adding a whole song to a video of your team (of whatever) playing a sport will in no way impact the original piece of work, it is very clearly a derivative, and should fall wholly and completely under fair use terms.
All of the Big Content guys have sued or DMCA'ed anyone they possibly could, regardless of fair use. They constantly fail "checks" that people put online - work that is absolutely fair use, and it still gets DMCA'ed.
I submit to you that in this situation, it is far more likely Viacom (or whoever) merely submitted a batch of DMCA's through an automated process that wrongfully flagged the same fair use (in this case, permitted) case.
This is money grubbing bullshit. Counterfeiting and idea theft are NOT the same as personal use.