While may not always be possible, the safest route is to QT
all animals that go into the main tank. As stated inverts cannot catch fish parasites but they can carry them if there is a hard surface to attach to. There is also the possiblility of free theronts in the water.
Best solution I have found that has not yet failed is only purchase inverts from LFS
tanks that are free of fish. No fish, no parasites. Better LFS
with larger set ups will actually keep their systems for fish and inverts seperate so they can treat the FO
tanks with copper or other parasite controls. I will generally inspect all inverts for hitchikers and possible visible parasites but I do not QT
In the case of the anemone though, I would not suggest a QT
period. I doubt it would survive unless you have a well cycled tank with the appropriate lighting. The theronts cannot attach to it and I highly doubt any water injested would be a concern. The problem to avoid is tanks with clown fish in them. Most wild caught clowns are increadibley cesceptible to carrying Brooklynella hostilis
If you go the route of buying from fishless sytems, you should have no issues.