It can't possibly be illegal or against YouTube guidelines to record/save a video or even less explain how you do it. That is identical to recording a TV show on your VHS recorder and that has been legal "forever".
Ahh, but you forget that the USA forced a change to all that with the introduction of the DMCA and has been globetrotting around, forcing parity with US copyright laws throughout the world.
While every time the issue
had gone to court previously over the years (the cassette tape recording of vinyl, the Sony Betamax case, etc.) the result was the proper one, allowing recordings under certain circumstances. The movie industry was
so worried about the death of theater movies if home video were ever allowed to become a "thing", yet when they "lost", it spawned the home movie rental market which overtook theater revenues and made them more money than they ever imagined. They never learned anything from experiences like that and continue to shoot themselves in the foot at every opportunity. Good riddance, I cannot wait for the implosion....
Now that media is
digital, "they" have changed the rules via the DMCA to say that everything is different now and you're essentially not allowed to record anything unless it is expressly allowed by the locked-down system provided by the overlords where recordings can be removed on a whim, etc.
For example, the guidelines for teachers who wish to show clips of something in their classroom is to use a video camera to record a television showing the desired programming and then show that recorded footage, thereby officially meeting the technicality of the rules to exercise their fair use rights, showing the media to their class for educational purposes.
YouTube hosts videos that are CC, hence by law you are allowed to download them. If YouTube does not provide a link and does not allow you to use third party tools, they are in breach of the law and that would invalidate their terms of services on this point.
Just because you are theoretically
allowed to download a copy of something does not mean YouTube has a legal
obligation to make downloads available. Official YouTube policy is "
NO DOWNLOADING, EVER!" and there is no law that forces them to add a download button. Downloading can still be a breach of their TOS and they can essentially do whatever they want to try to prevent it.
Remember, from big copyright's perspective you never
own any of the media content that you think you purchase. You simply are purchasing a
license to consume that media and they'll try their hardest to make you pay for that content as many times as possible.
I wonder how many people have paid for the same album on vinyl, then 8-track, then a cassette tape, then a CD, then one or more "digital" copies, often with DRM that ends up disappearing when some company goes out of business and shuts down their authentication servers, etc