4 weeks of "disease free" (!) symptoms is the minimum(8 weeks is best and safest and used by many professionals).
Why 4 weeks: 4 weeks is the maximum time that (most) anything pathogenic can go without being expressed (showing symptoms). Many nasties will die without a host within that time as with corals carrying in diseases on other organisms (like parasites on fish) on their surfaces and in their water (as with the employee that just took his hand out of the infected fish tank minutes prior to your arrival and request to bag your coral at the LFS
)
What else is QT for: screen for Montipora eating nudibranchs, predatory crabs/shrimp, worms... siphon out predatory flatworms, etc.
More reasons? The high light coral you just bought was collected over 10 days ago and transported through the chain of custody in near darkness since then (shipping bags, boxes and modest wholesaler holding systems). If you put this coral right in the display under bright lights, the animal will stress if not bleach in many cases.
There are MANY more reasons for QT, but just a few of these should be enough.
When someone says they got a rock or coral from another LFS or aquarist and it "infected" their tank with Aiptasia, etc... I remind them thats not true... they infected their won tank without a simple and conscientious use of a QT tank.
Please! QT always and without exception for all things wet (snails, LR, LS, cotrals, fishes, algae/plants, etc.)