The reason the AR coating is on the outside is if it was only on the inside it wouldn't block, or diminish, the reflected light hitting the crystal. There would be no reason to just put it on the inside as it would do very little good. Most of the anti-reflective properties are done at the surface exposed to open air. Although the surface that is coated is exposed and susceptible to wear and tear during wearing there really is no alternative way of doing it.
Anyway, good to see the OP got his watch replaced. Sometimes stuff happens which is not easily explained.