As it turns out disputing copyright claims on YouTube is not easy. I was notified that an audio track on one of my videos violates another artist copyright. Since this was a loyalty free track I purchased from a large vendor (SmartSound), I submitted a claim, but it got rejected giving me no other ways to dispute the decision. I tried to talk to YouTube directly and got a polite but negative result - YouTube doesn't handle these disputes by themselves.
Here is what I've found so far. SmartSound has a process for handling such cases: My Video was flagged by YouTube? but it would be best to obtain a copyright document before submitting your claim on YouTube. I'm still in the process disputing my claim, so I'll let you all know how it ends.