No, the limit of 1 region per server is a limit affecting all installed cards, not only the rezzed ones.
Page 13 of the rule book: "The Corporation can only have one upgrade with the region subtype installed per server or server root, as listed in the text box of these cards."
Huh, turns out I had this wrong. It's never come up, thankfully, but I'd always assumed it applied only to active cards, as is the case with unique cards.
EDIT: Also, both Dydra and Wh0isTh3D0ct0r could have handled this better. This was a genuine rules query. Wh0isTh3D0ct0r's initial response sounded accusatory, as though Dydra was intentionally attempting to cheat.
Sadly, it escalated badly, and I have to say Wh0isTh3D0ct0r handled it with better aplomb.
Edited by CommissarFeesh, 01 November 2013 - 08:54 AM.