There is no bandwidth to pay for. This is settlement-free peering. Once you have the line cards, it's simply a matter of adding the physical cross-connects.
Settlement free peering only happens if the traffic is balanced. In the case of Level3 and Verizon, it's not, hence Verizon's point (and apparently it was Level3's point when dealing with Cogent) is that the settlement free peering is not appropriate for such lop sided traffic and Level 3 needs to pay via alternative arrangement with Verizon.
It happens when it's mutually beneficial, regardless of whether the traffic is balanced. I have (free) peering w/ a few networks that are wildly off-balanced (on the order of 5:1 at times) simply because "free" is still cheaper than what I'd pay to send it to them over another (paid) transit link.
Verizon's position is that simply adding more cards within the free peering agreement will make it even more unbalanced in level 3's favour, hence their suggestion that level 3 pay for bandwidth through a different agreement.