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.
I think Level 3 is saying they'd be willing to pay for the cards, but not bandwidth, eg continue using the free peering agreement.
Verizon is saying that Level 3 should pay for the bandwidth (probably way more costly than the cards), since they are already getting more than they are owed in the free peering agreement.