My thought was mainly that there's no point in starting a witch hunt, just because the company is in the media business. I'm sure there are actually good companies in that business, and hating them all, just for the sake of hating them won't improve the situation. Having a few agreeable companies that the geeky public would like, would probably be to everybodys benefit.
I'm willing to give them the benefit of the doubt, since mistakes can happen. But this is a big fuckup, and as seen, it aggravates the already hostile feelings toward the media industry. So they need to come up with a really good reason why this happened, and something more than words to make sure it doesn't happen again, before they have my sympathies.
I'm sure this in not the only video with wrong automatic tagging. So they could e.g. go through all videos which are tagged with having their music. I don't care if it's 1k, 10k or 100k. If the music was actually not theirs, they will contact the owner of the video, and give them any ad revenue they have gotten for that video, and release all claims to the video. That would go a long way to convince me that they did not act maliciously, that it was a honest mistake.
And yes, I do agree that there should be big fines for wrongly claiming that the video contains your copyrighted material. Hell, I'd even make that a some % of the revenue of the company.