Should, by what standard?
Legally, under the DMCA, maybe Google has no obligation to provide this facility to UMG.
But as far as I can see, no-one is paying Google to host the content under debate on YouTube. That probably means Google has no contractual obligation to anyone to do so and is free to throw the content out any time they want for any reason they want, including any back-room agreement that might have been made with any big media firm.
If you want someone to do something important for you, and you're relying on free services on the Internet to do it, then you are typically entitled to a full money-back guarantee. Anything else comes with a price tag one way or another.