The apartment analogy isn't perfect, but it is a good example to show that just because you own something, it doesn't give you the legal (or moral) right to muck around with it whenever you please. If you're renting computer space to a customer, there are rules that need to be followed. Some of them are legal, some contractual, and some are societal norms.
In this case they definitely violated the societal norms and possibly their contractual obligations as well. I'd say that you have a pretty good expectation of privacy on a virtual _private_ server.
I don't particularly know anything about Rimuhosting. I know most places are oversold to a certain degree. I suspect that there isn't any way to make money in the industry if you're not.
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.