Don't know the Verizon FIOS DVR and its capabilities. By far the best connection of it to the Macbook would be Firewire: I'm sure the Macbook has it, don't know about the DVR. But if they both have these ports you should be able to feed the digital file on the DVR into the Macbook with no quality impact.
Failing that, what DOES the DVR have? How did you get your camera files into it in the first place? I'm thinking of my situation with a Sony digital video (tape) camera. It has an always-on chip that converts digital and analog between each other. So, for example, I can feed analog Composite Video plus stereo audio into it and configure it to feed that digital version of that right back out on its Firewire port. That signal can be fed into my computer's Firewire input for capture. So the camera becomes the analog-to digital "capture card".