I've never had this problem with cats however I did have this problem with a dog that I adopted from the shelter who had distemper and had to be put down.

Generally though I always excpect any cat adopted out of one of our local shelters to come home with a URI. They are usually in a cage, tons of cats in a room and they are stressed which causes it. Both of Alexa's cats had a URI when she adopted them and so did her sisters. But I don't count that as anything serious. So I voted that I've never had this problem.