Must be a third party retailer then that goes through Global Warranties.
I do see you point about whether it is or is not Verizon's fault.
However, think of it this way: When Verizon authorizes a third party dealer to sell their phones, they are taking it upon themselves to have their reputation based upon all actions of the third party dealer. That's why it is an authorized third party dealer and not a phone randomly bought on Craigslist.
Verizon therefore authorizes the insurance company chosen and that is where the responsibility in this case comes in. Where I bought the phone is less important than the brand name Verizon stamped all over my bills and paperwork. If they don't want the responsibility of third parties then they should only inhouse make sales.
Either way, the gripe is with the insurance company authorized by the third party authorized by Verizon in which I have been dealing with. If the insurance company fails to do their job, then it falls upon Verizon to take upon responsibility for the forced dealings with said company.