But are you really self hosting if you don't build your server silicon from first principles :)
I think in your analogy a VPS is more like renting a (normal) car rather than buying one - you're still in control over where it goes and its up to you to obey the traffic laws but if there are any major issues that are not your fault it's up to the rental company to make sure you get a replacement.
I'm curious what your goal is with your language crusade? Being precise with your language can be important when the distinction matters, but does it really matter here?
> If you depend on anything which has “cloud” in its name, you are not “self-hosting”.
What if it didn't have cloud in its name when I signed up but some marketing bozo adjusted the description since then? Did it stop being self hosting even though nothing technical about the setup changed.