You are correct. The 'verizon router' is only necessary in some strange way to support the set-top-box for TV purposes [1]. If you have internet only, and a hot ethernet jack on the ONT, you can use whatever you like.

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.