I have figured out that the difference is that when the the movie is published as flash, the allowedDomain callback (in Director) receives "localhost", but when it's published as AIR, the callback receives "app#myAppID".

According to the Director documentation if my allowedDomain callback returns TRUE (which it does), the incoming message should then automatically be processed. But for some reason this isn't happening when the domain isn't "localhost". Anyone have any suggestions?

FYI: I am using Director MX 2004 and Flash CS4 (AS3)