This time, they might be telling the truth
If Comcast is mostly cable (ie not fiber) then this would make sense as to how many other companies do it. The internet connection on cable is merely another channel or frequency on the cable like USAHD or CBSHD for example. What cable companies frequently do is put the internet on one channel and a private intranet for VoIP on another channel - so they are basically dedicated to each purpose and separate. SInce these frequencies have a finite bandwidth, they will never interfere with each other and never mix. They are probably even kept separate as VLANs within their network when they get to the head end. The only space where there might be contention is if they have to send the voip between different cities or facilities but I don't think that's a boatload of bandwidth.
I hate to say it since I think they are the devil incarnate, but I think they might be ok this one time.