The idea of an Apple branded DVR is possible, but I would say thats about as far as it would go (replace the cable company? fat ****ing chance).
The opportunity for an Apple DVR exists because of OCAP or now known as Tru2Way. Apple could build their own STB like TiVo has done, but integrate iTunes to allow people to buy shows and movies, as well as stream music and movies from iTunes around the house.
There are substantial issues however, one is engineering and support - TiVo is slow as molasses when it comes to engineering new hardware (the new DirecTV TiVo just got delayed again). For Apple, you'd probably have to re-engineer the AppleTV to use an ARM chip and a broadcom video decoder (which, IMO, they need to do anyways to cut AppleTV costs down so they can sell it at $149), but from there you're really only adding the cable tuner and hardware to communicate with the headend, and the Java software to run the OCAP platform.
The issue of replacing the cable company wont work because they will not let themselves turn into a dumb pipe while all your video comes in over the internet. They'll institute monthly transmission caps (250GB/mo or whatever), they'll make sure that their providers (Discovery, Viacom, Disney/ABC, Universal, etc) don't put shows on iTunes until the day after they air. So while everyone else it talking about last nights episode of Survivor: Mars, you haven't been able to watch it yet because it just came out on iTunes a few hours ago. There are a number of things they can do to keep iTunes from getting a leg up.