That's not true. If you're using an open-source distro and the vendor terminates the support agreement, you still have the source, so you can pay a 3rd party to maintain the software for you (e.g. by backporting security fixes from newer releases).

You can, but it will cost you 10x more to maintain the distro than it cost the original authors, and you won't be able to share the cost with many others. Worse, the cost will only increase over time. Not as dire as a closed source abandonment, but eventually you will have to upgrade.

You don't have to "maintain the distro" per se. You just have to backport security fixes for the subset of that distro's packages that you actually use. If you have a large organization and you only use a limited subset of the software provided by the distribution, it's not inconceivable that you might have the resources to do so.

That's simply unrealistic. It's a nice theory but if you're the only people using that software, how is it going to be cost effective to take the burden of maintaining it?

Well you have the same problem if the company that supplies the proprietary software goes out of business except that you are usually just flat out screwed. Granted it's unlikely that someone like Microsoft will go out of business anytime soon (but then again I'd say it's also fairly unlikely that Ubuntu disappears anytime soon and even that would leave you with a fallback option of other, similar Linux distros).

If say Windows XP just gets phased out on you that's not exactly cause for celebration either. And of course there's also the advantage that you can at least theoretically check most of the source code of Linux which is probably somewhat relevant in a government setting (a potential NSA cooperation of Microsoft says hi)

I see you've never encountered legacy enterprise software...