traffic parity with Verizon
Traffic "parity" is only relevant when you are talking about backbone Internet providers providing alternative routes in order to help make the Internet routing more robust. Basically an I'll scratch your back and you scratch my back mutually beneficial scenario where having two equal backbone Internet partners is more robust than having just one route over a long haul network. So for instance having a peering agreement with a company that has a wire from LA to Boston so that if your LA to Boston wire goes down, then your traffic can still get through.
But when you are talking about last-mile customers who are the ones initiating the requests for content, then peering is not about traffic parity, it is about providing your customers with the bandwidth to the content they want. As long as L3 is willing to provide adequate bandwidth connections to Verizon's networks in the local metropolitan areas, then they are fulfilling their end of the bargain as a backbone provider peering with a local ISP.
Sure, if L3 was just saying they were going to dump all the Internet Traffic destined for the East Coast in LA and Verizon could deal with getting it across the country, then that wouldn't fly. But as far as I know L3 is ready willing and able to send all the traffic across the country and put it as geographically close to the Verizon customers who are requesting the content as Verizon will allow. But it is Verizon simply saying they won't allow L3 to increase the bandwidth to Verizon Customers until Verizon gets a bigger cut of the action.