The fiber termination box they install has two ports they can activate – MoCA (coax) and ethernet. They really want to just activate the MoCA port, because that’s what their router and set top box expect.
You can only have network going over one of the ports, so generally they’ll refuse to activate the ether port, because their router and their set top box both want network over the MoCA port.
However, if you absolutely don’t want their router or their set top box, it’s possible to have the installer activate both ports and have the network go through the ether port. You’ll lose two-way cable stuff like video on demand, but I didn’t care about that at all. You end up having coax going straight to your TiVo or equivalent with a multistream cablecard, and ether going to your own router (I use an Airport Extreme).
I’ve had this done at two different houses, and it’s worked fine both places. Both times I’ve had to argue with them about it, though, and both install techs have had to call a supervisor to figure out whether I was just making things up.
I found out about this by accident – I first got FiOS before they offered TV in Pittsburgh, so I was network-only. The guy tried to convince me to use their router, but since at the time I had an already-set-up wireless network, I didn’t want to screw with it, and got him to run ethernet. Then when I added TV service, I did some digging and found that I only really needed MoCA if I wanted to use the shitty Verizon set top box instead of my TiVo.