If you rent an apartment, you don't call it "the apartment that I rent", you call it "my apartment". Also, the landlord owns the place, but that doesn't give the landlord carte blanche to enter the apartment anytime they feel like it.This analogy doesn't really hold. "Your" apartment gets special rights under the law in the US and probably other places. Those rights are actually pretty extreme (it takes months after they stop paying to evict someone in most states, for example), and you don't have those same rights or expectations of privacy within an office building, or anything else you rent or lease that isn't your domicile.
According to their terms and conditions, "Misuse of System Resources" is prohibited, but their only listed recourse is to "restrict, suspend, or terminate" the account.
Sounds, to me, like they restricted his account to one that wasn't running Apache.
But, I agree that they should have simply turned him off. Customers that don't want administrative assistance on the system should never have it imposed on them, and I would also prefer my provider never login to my systems (and I don't provide them with access to my systems; though I know that because they have access to the hardware, they always have root available to them; I rely on good faith to prevent them from doing harm or abusing my privacy).
However, that probably would have shown how oversold the machine really was.
While this is very often true in the VPS hosting industry, Rimuhosting has an otherwise very good reputation. It's pretty easy to know when you're on an oversold host, and it's not something I've ever heard Rimuhosting accused of.