Well, if you don't control physical access to your server, the data isn't safe.

Do you know if host's admin has typically an access to my data?

Typically the admin has access to all of your data, if he wants to. Even if he doesn't have by default, he can gain access to it far too easy.

That's OK if you want to host a private bulletin board, but not if you have a lawyer's data on your server.