The Betamax case was about stuff broadcast over public airwaves, whereas this is a medium that the RIAA barely tolerates, rather than the (ideal) main distribution channel. Seems like a big enough difference to me.
The ruling there doesn't seem to rule out making copies of shows from a cable network, which are not exactly public airwaves in the same sense I think you mean.
I don’t see the fact that the RIAA dislikes internet based streaming as relevant to the analysis. Downloading a publicly available video transmitted over a nearly global communications network is directly analogous to recording a show to tape from a TV signal.
The signal is broadcast (ie not under your control) and so the sole purpose being permitted there is time shifting.
YouTube is an on demand stream. It would be comparable to recording a pay per view movie that you purchased. Is that legal? (The question isn't rhetorical, but I seriously doubt it.)
That would be an interesting argument. I suspect it would be illegal because a pay per view stream is typically time limited. But if the stream itself were still valid while you were on the plane ... ?
"...this is a medium that the RIAA barely tolerates, rather than the (ideal) main distribution channel."
Right, this is the precise problem, and it has to be solved - not by a free-for-all but with proper equitabl copywrite laws.
As matters stand, it's only going to get worse. Say we assume that if somehow both YouTube downloads are made much more difficult to crack AND no downloaders are available, then viewers and downloaders will then use newer tech that's even easier to use to record the videos. With new hi-resonution 4k cameras becoming commonly available, they'll be able to record stuff with still-excellent resolution by just photographing the monitor.
Of course, that still won't deter the RIAA, I can see them trying to ban cardboard covers and jigs that hold cameras and
monitors accurately in alignment.