As far as I know, a legally enforceable "DMCA takedown" can only be about copyright infringement. However, YouTube is under no obligation to not honor takedowns that aren't legally binding.
I couldn't find the reference offhand but I've read that YouTube has no ability to adjudicate the validity of a DMCA takedown request at all. They must responed as proscribed by the DMCA.
Which makes sense because once the DMCA is involved it's ultimately a legal dispute between the person that uploaded the video and the person that claims to own the copyright. And that kind of dispute is something only the courts can decide.
If Jay-Z was not satisfied with the process, he could submit a DMCA request and YouTube would have to follow the DMCA requirements in processing it, but the current process is better for both of them (not for the posters of the contested content, though).
That's what's ripe for abuse. Why isn't it a fiduciary responsibility to their "partners" to make sure they aren't needlessly deprived of revenue, in situations where a 1st year law student could tell them there isn't a legal basis for the takedown?
The legal basis for the takedown is the language in the Youtube terms and conditions that says that Youtube can take down the content at their discretion. It does not matter if that decision is caused by a non-binding takedown request of a self-asserted copyright owner, or by a drunken manager randomly clicking to remove videos, the legal arrangement between Youtube and their "partners" does not assume any fiduciary responsibility to ensure that your videos will be kept unless absoltely needed, and no current law is forcing them to assume that responsibility.
I mean, the statement "why isn't it a fiduciary responsibility to their "partners" to make sure they aren't needlessly deprived of revenue," seems very weird from the perspective of law - why would there be such a responsibility? Do you have some law in mind that would cause it? E.g. CEOs have fiduciary responsibility to shareholders, stockbrokers have fiduciary responsibility to their clients due to specific laws, but in general there is no fiduciary responsibility between parties in a contract, the parties can be 'hostile' towards each other as much as they want.
The default legal position is that every private actor is free to act as they want for their own benefit as long as they are not breaking any laws or contracts. If I cause you some losses by doing things I am entitled to do, there's no possible liability - in order to claim damages, I have to have done something wrong. So in the absence of a specific law or contract requiring Amazon to ensure that their "partners" aren't needlessly deprived of revenue, that lost revenue is not Amazon's problem, and they're entitled to (for example) intentionally cause partners to lose that revenue if it benefits Amazon in some way and there's no statute or contract that restricts Amazon from doing so.
If YouTube stops taking down these videos based on this "fiduciary duty" and they get sued again, will this union pay for the legal fees and potential damages? Yeah, not likely.