I could be wrong, but I think you only need the Verizon modem if you also get TV from them. If you don't, you have to have them activate the ethernet port on the ONT and you can use whatever router you want.
My FIOS came with a hot ethernet jack, and the crappy verizon POS router has never been hooked up to the FIOS. Instead what is attached is the Linux PC that acts as my router/firewall. Works just fine that way.
[1] And, oddly, it (the stupid router) is still required for the set-top-box even if all one has is TV+Phone. It's coax has to be tee connected to the coax feeding the set-top-box before the set-top-box will start up and operate properly.