Sigh. I say that you've managed to make "improv" just mean "make stuff up" and therefore not terribly useful for discussion because all RPGs have making stuff up, and you respond to this by telling me I've never made things up. Because parameters, I guess, which someone make improv into just making up? Not sure. I don't see any value whatsoever in discussion how making things up improves RPGs -- this seems entirely banal and obvious. Further, I'm don't see value in pointing out that when you play and RPG, there are constraints on what you make up. Again, this seems banal and obvious.
Discussion ways you might make things up has some more value, but only if we actually discuss them as separate things -- if we're just going to smear any given approach into all approaches, there's no real value anymore. Likewise discussing how constraints apply -- discussing specific constraints has value but just saying there's constraints doesn't do much.
Improvisation isn't just making stuff up as you say.
It requires to listen to the players and for the players to listen to the DM.
I'm not telling you that making stuff up is the only way to improvise. Improvisation requires both sides to listen and act on what the other is trying to build. In a Role Playing Game, there are parameters that will restricts the direction improvisations might take. But in essence, with or without restrictions improvisation is an important skill in a DM's box.
As for constrain. The only real constrain in improvisation in a D&D is the campaign world. Other than that, everything is fair game. I would not allow a character to suddenly have a blood link with the king of a country because that player decided that it was good for him. There are limits on what a DM will allow. Just like I would not allow a player to suddenly be the secret lover of a powerful NPC so that the player would have a safety net if push came to shove.
Improvisation, especially from the players part, must be monitored carefully; especially if the players is not a regular one or an early addition. Some player will start with dubious backgrounds in search of a possible exploit to give them an advantage. I have seen that happen quite often when I used to have open games at our hobby store (before our Friday Night Dungeon became more of a show to let people see what RPGs are about). For 20 years now, I have not encountered such a player simply because all characters are made with my approval and/or guidance.
Also
Improvisation is not always right here and now. It can be long term, short term or even episodic and might happen over the course of a campaign. It does not always imply discussions with NPCs, sometimes, it is only events. A discussion with an NPC can be a total improvisation not following any guidance or preset parameters. Or it can be scripted to the very colon and semi-colon you can imagine.
A sandbox style game can be improvisation galore just as much as the sandbox itself will be scripted without the knowledge of the players. Where do you go? Left? Fine, my prepared adventure that was on the right is now on the left. The best DMs will make prepared stuff appear completely improvised and fully tailored to the characters at hand. This is the reason that improvisation is such a big part of RPG and even with preps, a DM needs to have some skills in improvisations.