For example, suppose there are 5 separate networks, run by different groups: A, B, C, D, and E. C connects to A,B and D, and D connects to C and E. In this case, the only way networks A and B can connect to D or E is through the connection between C and D.

Now, if in this arrangement, the D or E networks are sending/requesting a lot of traffic to/from networks A and B, while C is rarely requesting data from D or E, then network C might have a fair argument to make that D is abusing their balanced-flow peering agreement. Basically, they are being asked to be a middle-man for all the traffic going between networks that are NOT theirs. They might ask for compensation for doing this job (carrying traffic between two other networks).

However, this is NOT what Verizon does. All of the traffic between level 3 and the Verizon network is bound FOR A VERIZON CUSTOMER. They are not a middle-man, they are the end destination. Now, if Level-3 is sending data over those congested level-3/verizon gateways that is bound for, say, AT&T's customers, then they would have an issue and could fairly demand payment.

That is not the case, however.