Angatol, AA is saying the following:
1) If all of a passenger's travel within Area 1 is on AA, and the passenger travels via DFW and/or BOS, then the passenger gets a 1000 mile TPD.
2) If the passenger makes even a single flight on some other carrier, within Area 1, then the passenger does not get the TPD.
Certainly the transatlantic segment will have to be on AA. I think that's somehow implied on the fare rules -- can't apply an AA fare to a ticket that doesn't have AA on a long-haul segment. AA is saying it only wants to provide the TPD if all within-area-1 flights are also all on AA. This ticket allows for unlimited stopovers and unlimited transfers, so all kinds of crazy multi-carrier routings are permitted in principle. AA is saying that whatever you do, if you want the TPD, you must say on AA within Area 1. That's all well and good, except it remains disputed whether this provision actually appears in the routing rules. Hence this thread!
Regrettably I don't know any TA's who I can ask for this routing rule. I relish EF exactly because it provides this information. I've never had the problem of anyone alleging an EF statement of routing rule is incorrect or incomplete.