Amazon Prime is coming in on a different handoff where the Verizon links are not as saturated.
Anytime I've done traceroutes the problem is at the handoff point - first hop outside of the Verizon network. If Verizon customers are requesting X mb of traffic and Verizon only has the infrastructure at the handoff to accept a subset of X then packets are going to be dropped and service for clients will deteroriate. That is what is happening with Verizon.
The best thing in the world for consumers would be for the spat between Verizon and Netflix relative to the C&D letter to go to court. Discovery would go a long way towards documenting that Verizon is the bad actor here.