I've got this many times, myself. The content I have problems with are creative commons tracks by independent artists that I know for a fact are not owned by the labels asserting ownership.
The primary issue is this: YouTube, probably as a part of their deal with the labels to keep copyrighted music videos on their service, has given the labels too much power. Under the standard DMCA model, the copyright holder files a complaint, the video poster would contest it, and then that would essentially put the matter out of YuTube's hands. The label would then have to sue the person who filed the counter-claim if they felt they had a case. Under the current YouTube system, the label has the power to say "Nope. We reject your counter-claim. It's our stuff."
At that point, you are officially out of options. In most cases, your content gets to stay up, but it becomes monetized and the ad money goes to the label rather than the video-maker. Occasionally the soundtrack will be muted or blocked in certain countries (Germany, most often) but usually the notice just means more money for the labels and nothing else.
While I can see how that system might sound like a decent set-up since it means that YouTube gets to keep the copyrighted stuff *and* its users don't have to worry about being sued if they file a counter-claim, the problem is--surprise, surprise--the labels are abusing it. It is apparent to me that counter-claims are rejected virtually every time (only the labels have this power, if the copyright claim is from a 3rd party entity then a more standard DMCA model applies). It seems apparent to me, based on the rejections I've gotten, that the labels are simply not acting in good faith. They haven't quite automated the process of rejections, as that would be too flagrant--but whoever job it is to review the claims has apparently been instructed to simply reject them all out of hand.
Give the labels a financial motive to misbehave and, guess what? They will. It shouldn't surprise anyone. Remember when they took-down Tech New's Today's video covering the takedown of the mega-upload song. It included a sample of the song. It was newsworthy, and thus obvious fair use. The labels' defense? They didn't remove the videos on copyright grounds, but rather because they *wanted to*. They assert that their agreement with YouTube gives them the *right* to remove any video they want for any reason they want. YouTube may (I say, "may" because, as far as I know, they've been silent on that claim) disagree with that interpretation, but honestly its certainly not far off from how the labels are acting.