Full disclaimer: I'm not a lawyer, I'm not your lawyer, and I'm just a law student.
I've been interested in this topic for a while, mostly because I have an affinity for areas of the law that stand to be tested as a result of new capabilities brought about by the Internet. I also have a morbid curiosity regarding judges' interpretations of laws as applied to factual situations that they may not understand, or my favorite, condense and equivocate to a factual situation rooted in "traditional" legal analysis that they deem synonymous with the situation. I'm not ragging on judges here or calling anyone ignorant, I'm simply stating that the Internet does raise complex, untested issues that require either a rewrite of the law or a force-fit into something already on the books. These are intelligent, experienced, and well-educated people applying the law to difficult fact patterns.
That said, it's probably illegal. However, it's not well tested. To my knowledge, there haven't been any federal appellate decisions squarely on these issues. As a matter of black letter law, it does look like a copyright violation. There's a pretty obvious nexus between your own timeshifting of content versus downloading it off of the web. As a practical matter, however, maybe you'll be the first or maybe not. The RIAA and "making available" theory isn't well tested, and where it has, it's tended to fail or get broadsided by collateral issues. I doubt that these would have much weight anyway, since the other moving parts in those cases seemed to cloud the issues. The other cloudy issue, and what I think might be a point of controversy if one of these went forward, is the damage calculation. For something originally on broadcast tv, for instance, a strong argument could be made that it's nominal and any statutory damages may not fly.
So the real answer is, who the hell knows. It's certainly a close enough call that there is a plausible cause of action, so I imagine someone will eventually get sued and take it up the ladder. Thing about the media assocations, though, is that they tend to favor defendants with no money, or at least not enough to cover their costs of a jury trial, let alone the appeals.
Second disclaimer: I've had a couple of Birthday Scotches this evening.