Two things first: one, I don’t want to start a debate about right or wrong; I’m just asking about legal issues. Two, I’m working from two assumptions here, either of which might be wrong. Feel free to call me a doofus if they are, and I’ll be glad I learned something.
So, the assumptions:
If you watch “traditional”, programmed TV, the rights have been cleared for that particular moment of broadcast. This is different from, say, a DVD that you bought, where you essentially buy the rights for you and your household to watch the content from that particular medium as many times as you want until such time as the medium breaks or becomes obsolete. It follows you are not allowed to record a broadcast, as that would violate the “at the moment of broadcast” proviso.
Things like DVD recorders or VCRs are only legal (see assumption 1) because, technically, you can do non-illegal things with them like copy home movies and… um… well, copy home movies, certainly.
Working on those assumptions, we now come to TiVo or other digital TV recorders. These have only one purpose: recording broadcast TV so you can watch it at a time not defined by the programmers. They don’t do anything else. So (aside from the fact that I couldn’t live without my digital recorder) what am I missing that makes these things legal?