It's not like somebody showed up at their office and said "Here's a giant pipe, push all you want".
And "they're not paying to the right people" is an incorrect argument. You pay _your_ connection point for money, and the recipient pays theirs. Intermediate connections need to be handled by the respective networks, not the endpoints.
So if Verizon wants money, they need to extract it from their peers, not Netflix. (Or the user). Which they don't do, because, well, turns out they make enough money of it that losing a peering agreement is actually detrimental to their business.
It's completely within VZWs rights to expect money from Layer3 for peering. It's not within their rights to extract it from somebody three hops down. That is the _reason_ we have peering agreements, billing individual customers doesn't make sense.