Your understanding seems to be correct as far as peering agreements go, but the implication that this is what is being disputed is incorrect.
If it was correct, then AT&T (and Comcast) would be saying that Cogent wants a free lunch.
Netflix has an agreement with Cogent (No free lunch there), and Cogent has an agreement with AT&T that AT&T is not happy with. That's as close to objective truth were going to get here, and it needs sorting out but that's really a matter between Cogent and AT$T, what follows is what we should really be discussing:
If the issue is Peering, then its a Cogent-AT&T issue. Why is AT&T PUBLICLY SHAMING Netflix? And Just who is responsible for Netflix traffic?
Netflix doesn't just "flood" AT&T's network with data, rather, its AT&T's customers who request data from Netflix isnt it?
The fact that AT&T's subscribers are the ones that create the high demand for data is being completely glossed over here because then AT&T would have to argue that as it brings more customers on board, who came to AT&T for the Netflix BTW, then Netflix is being greedy because it won't pay AT&T for what is customers paid AT&T for!
And if that arguments reads as tortured, you're right, which is precisely why AT&T is framing the discussion another way!
Yes there is a peering agreement that needs to be settled. No, its not between Netflix and AT&T.
AT&T just wants to shame Netflix into entering into an agreement directly with them ($$$).
This is why net neutrality both matters and is at the very core of the argument here.
When AT&T can hold its customers hostage form a provider and claim a tithe on both, everybody suffers.