does your DVR have 'component' input
if their box has component output available, i suspect component input will record the signal
anything going to your TV from the box has to be Decrypted
how ever, HDMI usually has HTCP which means it will not record without an HTCP stripper box between the source and the recorder
as HDMI ports have HTCP signal recognition built in, freakin DRM (digital right management)
and yes you will to use their box to watch TV, you can place the DVR between the box and the TV if it has 'pass thru' so you can watch while recording
but you will be using 'component' cables not RF, not HDMI and NOT A/V
i suspect the RF and A/V will be std 4:3 SD signals
component carries 3 signals for video and requires 'separate' wiring for the audio
as for being required by the FCC to encrypt, i think that 'HOOEY',