That AHA doesn’t “get” Anglos is well known among the American Anglo breeders. While some American AA’s are the result of TB/Arab F1 crosses, those involved with the Anglo Arab as a breed rarely make such crosses and utilize stock that have been bred as AA’s for generations. (FWIW, most “Arabian folks” don’t know what an AA is; they tend to think of them simply as a type of HA and don’t know of the tradition and history of the AA.)
Given AHA’s lack of comprehension of all things sport horse (just try to get the AHA “Powers That Be” to understand that a Hunter is different from a Dressage horse is different from a Jumper!), I don’t find it all surprising that AHA’s AA registry has not applied for membership in the WBFSH, but the actual AA breeder’s in America do understand what they are breeding (hence the use of some French AA’s in American AA breeding!).
FWIW, AHA registered American Anglos CAN be presented to a number of the North American WB registries (including ones that ARE affiliated with their Euro registries) for breeding approval. (Heck, purebred Arabians can be presented to a number of the Euro based registries --both in NA and in Europe-- according to their rules.) Since the number of American bred horses being utilized in Europe for WB breeding is almost nil, that American AA’s are not being imported to Europe is hardly surprising. 
