True in a sense
What Verizon says is true in a sense -- from what I've gathered of this situation, Netflix's slowdowns are not happening within Verizon's network, and Verizon is not throttling the traffic.
However, Netflix has plenty of connectivity to these peering points, and are paying for every last bit of it (I have to mention this because US ISP propaganda now is to claim Netflix et. al are getting a "free ride" or "not paying their share"). It is Verizon letting their connection to these peering points hit 100% capacity and failing to upgrade it. They think (even though Netflix is already paying for adequate connectivity to peering points) that they should be able to double-dip and demand that Netflix pay a second time to pay Verizon to upgrade their connection, rather than Verizon allocating some of those numerous profits they make from their own paying customers to maintain the connectivity the customers are paying for.
I mean, I wouldn't get away running an ISP with a 10gbps fiber backbone and some 1.5mbps DSL links to the internet at large, then go around demanding Google, Amazon, etc. all pay me to upgrade the 1.5mbps DSL lines, would I? This is *exactly* what AT&T, Verizon, etc. are expecting to happen; charging customers for internet connectivity, but pocketing that as profit and expecting third parties pay for the internet connectivity instead.