And what if I am a paying Google Apps Customer. Video through youtube is included in what I pay for. Should UMG have the right to control that as well?
I think it would change the situation significantly if the organisation whose video was pulled in this case had actually been paying Google to host it for them on some sort of contractual basis, and the reason for Google's removal of the content was not a legal obligation but another private commercial deal.
Access to other parties videos? Is not.
And the party you contracted with (Google) has contracts with other entities. Has nothing to do with "rights". If you have a problem with the contracts entered into, then act accordingly.