Just to clarify a few things here.
First, YouTube has licenses from all the major performing rights organizations (ASCAP, BMI, SESAC), so the public performance is licensed, whether it's sung by a teenager or a professional. That means Warner Music must think some other right is being infringed. Reproduction? Derivative work? They don't tell you when they send a DMCA takedown notice or submit a fingerprint for automated Content ID matching.
Second, if you look at the four factors, the video is plainly noncommercial. It certainly doesn't displace sales of any professional versions of the song. And it also doesn't threaten any plausible "licensing" market, since I don't believe that music publishers are in the business of granting licenses to teenagers making noncommercial videos. I think those are the two most important of the factors here, and both favor the YouTuber.
And, finally, do we really want a copyright system that *discourages* people from engaging in this kind of creativity, especially when it doesn't hurt any existing commercial markets for the copyright owners?
I've met Fred and he seems like a pretty sharp guy, so I probably should have assumed that he had a reasonable point.
Anyway, a few notes here. If YouTube has licenses from the performing rights organizations, then (as I understand it), then yeah, this performance would be licensed. And since this is just a cover, then it's not at all clear what about this video Warner has a problem with.
With that said, while the performance itself is noncommercial, YouTube certainly makes money from the video from the advertisements they show on the page. As I understand it, the publishers go after bar owners who have live music, even if the musicians themselves aren't paid, so I'm not sure the situation is that different for YouTube's position vis-a-vis the publisher, at least ethically, which is a different matter from legally (though again, as Fred says, they have a license.) As for what kind of copyright system we want to have, I think it's pretty clear that we do have the kind of copyright system that discourages people from engaging in creativity.