I disagree. It is possible that the parasite was nestled within some frags
due to the fact that the originating tank had ich. It is not common, but it can definitely happen. No amount of stress is going to "cause" ich if the parasite is not present in the system. It is not like a disease that just appears, it must be introduced.
As far as adding new additions to the tank, you could always set up a QT
for corals and inverts. You would never use copper or hypo, but if you acclimated them in that tank, kept them in there for 6-8 weeks, then you could introduce them to the main and be very confident that you are not introducing ich.
That might be a little overkill, but if you want to be absolutely sure, that's what I would suggest.