I don't see why not. A ship with no special affiliations arrives at a starport. Can it buy unrefined fuel? Can it buy refined fuel? Can it have minor repairs done? Can it have an annual maintenance overhaul done? Can the captain have a ship's boat built? Can he have an extra ship built? The answers to these questions should be easy enough to get and should enable you to to assign a starport class. It doesn't matter to the starport rating why you can or can't buy something; what's important is that you can or can't.In a polity the size of the Imperium there are going to be all sorts of strange and unusual combinations of governmental, private and public facilities available. The rules can't possibly be expected to enumerate and detail every possible combination.
It's not the rules as such. It's the resulting setting fact. Why does Forine not sell refined fuel, repairs, annual maintenance overhauls, ship's boats, and starships to passing strangers1? For some worlds "because it can't" is a good answer, but I don't think it works for Forine.I can think of half a dozen reasons why a dictatorship might want to restrict the publicly available facilities while allowing and maintaining more advanced facilities for other uses, possibly including special economic or military purposes. I don't expect to need special dispensation in the rules for every one of them.
1 Strangers with the requisite funds, that is.

Hans