Verizon entered this contract with ESPN to be able to sell ESPN content
Typically, these contracts are of the sort where Disney says if Verizon wants to carry the Disney channel, they must also carry all the ESPN channels @ a certain rate etc
I also don't see your analogy as being the same. Customers pay Verizon for the bandwidth and Verizon is a customer paying Disney for Disney, ABC, ABC Family and ESPN* but with the added bonus of being required to buy them all to get the ones Verizon and its customers actually want.
You're correct in that it's a contract dispute between Verizon and Disney, but w/o actually seeing the contract we don't actually know who's in the right. My guess is that Verizon found a loophole and Disney isn't happy about it.