Ich is often associated with stress because stress weakens the fish, which allows whatever happens to be lurking the opportunity to pounce. Tangs have a naturally thin slim coat, which is bad for them combating parasites. Stress can not "create" a parasite though, so if you have a tank with no Ich and you put a fish in that is Ich-free, the system remains Ich-free. You can however add a fish that does not appear to have Ich (but that does and is just not showing symptoms) and then the system is contaminated and it can go after other fish.
This is why QTing new fish is important. Taking a fish from your LFS
that appears healthy and dropping it into your tank can cause problems. I made that mistake a few months ago with one fish, it ended up with MV and wiped out my tank (except for two Chromis that are currently in QT).