I was wondering this too.
It seems those PCI and USB tuners for your PC are really just relatively simple adapters that collect the signal from an aerial and convert it to a digital signal (USB/PCI). The PC does all the work making it into an image, that's why you need a fairly fast PC to display a HD station.
Tuners in a standalone TVs (portable or not) and set-top-box have to decode the digital signal into a displayable image themselves, hence they require some fairly fast CPU power. The set top box I have has a 250Mhz ARM based CPU, VRAM and 16Mb of flashram for the firmware/menu system as well as USB connectivity for firmware updates. It's effectively a small, fast embedded computer.
Interestingly, when using an Amiga with a small digital TV, the TV has far more processing power than the computer attached to it.