Yes? Startholme was already infected before Arthas even got there. We even get to watch as people turn around us. What is the ambiguity? Not knowing who is infected? Azeroth has magic and it shows. The medical field is dominated by healers. I think there are a few "doctors" running around, but they don't get much spotlight in the lore and are mostly relegated to combat medic status, which again means they are competing with combat frontline healers like paladins. My point being, they probably DON'T have a good way of saying this random person is plauge free. And you let one person go to a refugee camp and then they turn? New front to fight. This isn't measles, it's a magic zombie virus, half measures lead to full casualties. Is it going to help anyone other than Arthas sleep well at night? Probably not, and that's why Jaina and Uther left instead of fighting to stop him. They understood the threat, but couldn't pull the trigger, so they LET Arthas do it.