I'm already getting BBC iPlayer on the BBC Beta page and I am on cable... It's very handy if you miss a program. You can go back seven days and just watch the program there and then or you can download it and keep it for thirty days. Than I assume it vanishes in to thin air. I am pretty sure you can't copy it to DVD.
Technically You probably could copy it to DVD (its only a WMP file), but I doubt you could get it to play. iPlayer looks for the licence to play the program from the BBC's web site (so unless you can burn that to the said DVD as well, it wont work).
When downloaded it doesn't vanish into thin air, after a set period (the licence to play it from The BBC's web site does).