Regardless of whether Youtube has a history of removing content, my (non-lawyer) reading of the Terms indicate that they definitely reserve the right to remove videos at their leisure. The agreement grants Youtube a license to all submitted content, but, as far as I can tell, makes no guarantee about how Youtube will display that content, if at all.
Even if they haven't removed uncontested legally uploaded content before, the Terms seem to say that they can, and this might constitute the first time they'd want to. (See x0x0's sibling comment for cases where they've removed contested legally uploaded content, but I think you're probably talking about uncontested videos, right?)
(Incidentally, the EULA/TOS distinction feels really pedantic to me. The name isn't the issue here; we're concerned about the content of the agreement.)
it's your claim -- that youtube won't take down videos within their TOS in order to blackmail rights owners -- so don't roll in here, make the claim, then demand people provide evidence to the contrary
oh, and given their well documented behavior with regards to handing large rights holders the ability to take down videos because of music without issuing DMCAs and with no review from youtube, not hard to believe [1] [2]. (See how I made a claim and I substantiated it?)
Any allegations to the contrary would require proof on your part.