The backup provision applies to “computer programs” only. Not TV shows, movies, music, stage plays, player piano rolls, etc. (The relevant law is in 17 U.S.C. § 117 a.)
Maybe courts would find that fair use would allow the copying I described above. After all, in the “Betamax Case”, the Supreme Court found that at least in many circumstances, timeshifting can be considered fair use. The Supreme Court’s decision can be seen in this document. The first sentence of the last non-footnote paragraph of page 13 (part of the same opinion written by Justice Stevens) reads “When these factors are all weighed in the ‘equitable rule of reason’ balance, we must conclude that this record amply supports the District Court’s conclusion that home time-shifting is fair use.”
But they would have to read pretty thoroughly between the lines of federal law to do so. (And, again, that sometimes happens like in the Betamax case. But…)
So, it’s far from certain what the courts would think about that sort of use.
(Again, NAL. I kindof geek out on this stuff. Lol. But I don’t even have a shadow of a fraction of enough expertise to give any legal advice on this.)