Everyone (that I know of) is having the same problem. There are thread here, reddit, and dozens of other sites, yet Verizon refuses to acknowledge the issue either here OR via customer service.
All I can get out of them is "Well, if it's only Youtube, it must be their fault."
It's a chickensh1t copout, and anyone who works for them **bleep** well better admit it.
I'm in the process of changing ISPs because of this one issue, and the failure of Verizon to take action or even admit to a single user that there is a problem.