Not seen any of those videos (bandwidth low on this connection, not worth it), but I've seen stunts with both planes and light helicopters landing on moving vehicles. "Staged stunts" in isolation as a purposeful and actual continuous event, not just fictional scenes that could have accomplished their appearance through clever editing of less exciting component shots[1].
Undoubtedly it's possible to do (...and has been, as I said), although whatever you've seen (again, can't say for sure) could be as artificial as what happened in the "Trapped In The Sky" episode of Thunderbirds (first episode, first series, IIRC). Which was exciting. Good job they had the backup vehicle[2], eh?
Unlike with International Rescue, I don't see it as something you'd be prepared to send out as standard resource along with the fire-trucks at any international airport of your choice, though (even for smaller aircraft needing just the single landing platform). In a real-life emergency, where you even
have the time to prep for this, a driver willing to risk his life on an unplanned, untrained-for and un-rehearsed stunt is going to be an unlikely thing this side of the silver-screen. If it has at all happened and been successful, I bet it has also failed and been disastrous many, many more times than that with a healthy dose of "I told you so" comments from the ultimately prophetic naysayers. And (as also mentioned) aviation fuel can generally be dumped[5].
(I can only imagine how many different random training scenarios those Tracy boys must have gone through in order to have been prepared for just such a situation on their first outing... No wonder they're largely reclusive, apart from the odd extreme sports or motor-racing venture... I'm surprised they find time to sip drinks alongside the Thunderbird 1 launch pool at all, with dad Geoff getting them up to speed... Sorry, it appears that my Fandersonesque geekiness is showing... I used to be able to tell you what happened in every
single Thunderbirds episode[3], but that skill is now less acute and my memory more hazy. Of course, any gaps in knowledge that I have are doubtless fillable from Wikipedia, these days... Such is progress.)
[1] Planes and helicopters can be flown close to a the ground and a 'target' vehicle, switch to a close-up shot of the skids or fuselage seating itself (without seeing that there's a rig just out of camera-shot accomplishing that 'landing') and then away to a wider shot of the seated (possibly installed when at stand-still) aircraft being carried aloft the target vehicle. As mentioned, CGI assistance is also available to create the sequence.
[2] IIRC, that piece of drama was unscripted, and actually happened due to failures of the original model setup. Still, it either created or conformed to classic "Yes, we have a clever solution to the disaster... oh no, it's not working... try again harder/try something new!" formula which pervaded absolutely every future incident in the classic series. So by (bad) design or (no) accident it worked out for the best in more ways than the purely fictional one!
[3] Save for the one called "The Mighty Atom", which I seemed to keep missing, whenever it was on TV, both originally and during very rare repeats over the next couple of decades. I only ever knew the episode name. I finally got to see it when I got my hands on a full VHS boxset. You don't need to know that, but I'm telling you anyway.
[5] Without an "Alias Mr. Hackenbacker" device... to once more drag in some Supermarionation fictional facts. The trouble with Fireflash, however, was that there was a bomb (albeit that it was purely bait and may have even been intended to be dud) on the landing gear of the
atomic-powered plane, thus making a risky but not unknown (IRL) belly-landing attempt far riskier...