What does it do with it then [...] is an orthogonal question.
Hm, ok if we take the word "distribution" for it lexical meaning then maybe, although wouldn't that be "distributor"?
In this field "distribution" is the set of things that constitute the software package, by extension, in the case of free software, it is more a synonym of "flavor" since anyone can redistribute with their own changes added on top. You wouldn't call a supermarket a Cocacola distribution, it's a distributor, but the drinks themselves are the distributions (tho in my mind "distributed" sounds more fitting at this point).
If having a system of OS and server, both property of one maker, where the server distributes a form of an OS x (even just the source code) and the client OS can download those files, make the OS a distribution of x, then I can set up a computer with e.g. OpenBSD (with my own modifications to make it mine) that downloads an Ubuntu ISO from my server, then I load up that ISO into a virtual machine and now I magically turned OpenBSD into an Ubuntu distribution??
You wouldn't call a supermarket a Cocacola distribution
Only because it's kinda unconventional to buy oneself some Coca-Cola by purchasing an entire supermarket.
I would still call a combo meal "a Coca-Cola distribution", and whoever sells it to me a "Coca-Cola distributor".
I can set up a computer with e.g. OpenBSD (with my own modifications to make it mine) that downloads an Ubuntu ISO from my server, then I load up that ISO into a virtual machine and now I magically turned OpenBSD into an Ubuntu distribution??
my server
You're now a distributor of Ubuntu (regardless of the OpenBSD-based thingie), and your version of OpenBSD is an Ubuntu distribution. If, however, your hypothetical OpenBSD-based distro pulled all the Ubuntu bits from ubuntu.com, it would've been just an distribution of an Ubuntu installer.