It depends what you mean by real. Cable and Satellite companies compress their signals, but I would not call them crap. Granted, if you could pick up the OTA signals it would be slightly better, but even a compressed HD signal is far superior to SD. I think 98% of viewers would be hard pressed to spot the difference between compressed and non-compressed HD.
I think you're wrong on two fronts:
Cable, or at least Comcast cable, is not additionally compressed beyond the initial compression done at the broadcast station. In other words, it should be the same as off-the-air (OTA), but maybe a little better since it shouldn't lose as many packets in transmission.
Regarding the public perception of compression, it is quite noticable, even by Joe or Jane 6-Pack. Where it is most noticable is in moving scenes - like in an action sequence or anything with a panning camera. These scenes result in massive macroblocking - think of it as ugly digital blurring.
A case of this being noticable is when KQED, my local Communist Propaganda Outlet (otherwise known as PBS station) switched their night-time profile from one small SD subchannel and the rest dedicated to HD, to (at least) 3 (? or 4?) full-time SD-subchannel with the rest for HD. Everyone now comments how horrible the once pristine HD channel now looks. What once was a joy to behold (for non-political content) is now an unwatchable mess.
They supposedly are using advanced bit-tweaking hardware to "steal" bandwidth cleanly, but it isn't working. All this to run PBS-Kids, Spanish programming, and another PBS (largely propaganda) subchannel 24-7. Insane.