You are correct, distributions like Kubuntu are not TRULY community-driven as they are still subject to Canonical's influence. Anyone saying otherwise is merely being pedantic.

However it's not Canonical who's running Kubuntu, it's the community, they have the power to revert Canonical's bad decisions, sadly by giving themselves an increasingly higher workload. Most distributions will simply give up at some point, for example VanillaOS' next release will be based on Debian as it was getting too tough to remove snap and all the bad things Canonical adds.

Kubuntu uses snaps which are largely disrespected by the community, that's the end result of being under Canonical's influence. They can't rebase on Debian without effectively killing their raison d'etre and they don't want to remove Snap, perhaps because it would be difficult but most likely because they're deep under Canonical's influence, they look up to Canonical to some extent.

This is, in fact, the very meaning of "influence". It's even worse, in fact, much, much worse for Fedora, they have been culturally enslaved by Red Hat, sorry for the strong word.

It boils down to who and why someone is distributing the software to you. A corporation expects to eventually get some profits out of its actions, so it'll sometimes do things against the best interests of the users, because they benefit itself; on the other hand you expect a community-driven distro to be made by a bunch of people who just want to use the software, and have a vision on how it's supposed to be.

Canonical suddeny made Ubuntu closed-source?

Canonical can't make Ubuntu closed-source. Most of the code in Ubuntu was not made by Canonical, but by third party developers; Canonical is just grabbing that code and gluing it together into a distro. And most of those third party devs released their code as open source, and under the condition that derivative works should be also open source (the GNU General Public License - note, I'm oversimplifying it).

What Canonical could do is to exploit some loophole of the license in the software from those third party devs; that's basically what Red Hat is trying to do. In the short term, people would likely shift to Linux Mint (itself an Ubuntu fork) or make their own forks; and in the long term, fork another Debian derivative to build their new distros from it. (Or adopt Linux Mint Debian Edition.)

Even in community driven distro there are often many contributors that do so because parts of their livelihood depend on it. So it is not quite fair to say that there are no financial incentives behind it.

Its basically a question of relative scale. If there are lots of smaller companies and some hobbiists contributing it is called community driven, but if a single large company or their employees run most of the show, it is not.

Large gray area to be honest.

E.g. Wikipedia is community-driven because people contribute individually without a lot of coordination and without anybody telling contributors what to do, same for game mods. I guess by "corporate-driven" you mean there is a hierarchy and people whose job it is to do what management says e.g. Wikipedia foundation runs the infrastructure that hosts the community content and the same for most games. I'm not sure I'd call it "corporate driven" unless it has board members and investors demanding a profit such that they influence the decisions downstream, like reddit.

The key is in the name. Whoever distributes the software to you determines whether it's commercial or community. Where they get it from is irrelevant because they're the ones distributing it to you.

Ubuntu can't be made closed-source because of the licensing of the software they use from upstream. Red Hat is still not closed source, for instance. Everyone who gets it gets access to the source code. But if Ubuntu went away or whatever then downstream distributions would be in a spot of trouble. They could rebase on Debian (which is what Ubuntu is based upon), but how hard that would be varies wildly depending on distro. Linux Mint already have a Debian edition, for instance. No problem there. Pop OS would certainly be able to make it work as well; they're a very professional operation. But take, for example, Endeavour OS. It's Arch with a graphical installer and some nice defaults. Without Arch Linux (which is almost certainly not going anywhere and is a community distro) they'd have some real problems. There's no upstream to Arch to rebase on. They'd have to so fundamentally change everything to accomodate a whole new base and packaging system that they'd basically be making a whole new distro.

what would happen to distribution X if Canonical suddeny made Ubuntu closed-source?

I believe Linux Mint has done some planning for if Ubuntu does something like that - probably to rebase off Debian in that case

From what I understand and to continue your example of Ubuntu-based distros:

As you say, Ubuntu itself is corporate-driven, so there are things in there that exist pretty much solely to benefit Canonical (e.g the telemetry they recently introduced if i recall correctly)

Most of the time when basing distros off of others, I think it's to keep a lot of features - either to save dev time or because they only want to tweak a small portion of the distro and not write a new one from scratch.

Because devs can modify the entire codebase, they can remove features that are corporate-driven (telemetry and such) and effectively create something fully (or mostly) compatible yet without such features.

Another major example imo is the removal of snaps, which most people (myself included) strongly dislike - as far as I'm aware removing them in Ubuntu itself is quite a difficult process as it's baked into the distro itself. I imagine a lot of people want something like Ubuntu as it is quite friendly and has one of the lower bars of entry for Linux, but object to corporate things like telemetry and the overall monstrosity that is snaps.

Apologies, i went down a bit of a tangent, but I hope that roughly answers your question!

It still qualifies as community driven since they have no financial incentive to keep maintaining their version of the distribution, but they would certainly be affected by the upstream messing with how the source is provided. What they could ultimately do would be "hard forking", i.e. taking the available state of the original project and keep developing their own version on top without ever keeping in sync with, say, Ubuntu anymore. Instead they will become their own thing that at some point will have strayed from the original significantly enough to be fundamentally different in their packages, configurations, repositories, etc.

Additional community distros not mentioned: OpenMandriva, PCLinuxOS, Mageia, NixOS.