The Leviim are just as much owners of the land as any other tribe. The cities of the Leviim were apportioned to them by lottery in the same way as the rest of the land (see Malbim Yehoshua 21:2) and they were complete owners. However, you may be right in thinking that their ownership might be different in this regard. The Gemara tells us that ארץ ישראל מוחזקת היא מאבותנו and a firstborn got double portion from the land (see Bava Basra 119b). Thus, one could say that initially the land was the property of the entire nation, but God removed the ownership rights of the Leviim until after the division of the land. Thus, the Leviim were not among 'original partners' in the land like the rest of the nation, and might be considered like citizens of other countries, whose king allows them to live there.
However, when the Ran (as well as his source, Shut Baalei HaTosfos no. 12), says that a king cannot force laws upon Jewish citizens of Israel, his actual reasoning is because the king doesn't own the land and therefore cannot evict his subjects and has nothing to do with partnership. This is (I believe) clear from context. Therefore, when the Ran says that 'all of Yisrael are partners in the land', he doesn't mean that they are literally partners, or that a 'partnership' is a necessary part of being excluded from a king's edicts. He just means to say that it is not owned by the king. (In Yeshiva-speak: "I'm saying that the Ran is lav davka, and it's clear from the context that he's lav davka").
Furthermore, even if the initial 'partnership' was necessary for the Jews to be exempt from governmental edicts, that's only because their ownership (as partners) preceded that of a kings. This is equally true of the Leviim as well, because despite not having an actual ownership in the land (במוחזק) the people of Israel - king included - are obligated to give up some land for the Leviim (like a tithe, see Malbim Yehoshua 13:33). Thus, the king has no right to evict the Leviim any more than a Jew from another tribe.