Eh, who cares? It's a contract of adhesion and limits the airline's recourse in any case.
Without putting your AA number in the DFW-BHM-DCA itinerary, you certainly have less chance of a match being made. They may well use other identifying information like credit card used for booking, phone number, etc.
Worse case is they cancel your DFW-BHM segment.
American is indeed aggressive about detecting overlapping reservations and I'm not convinced that just removing a FF# will fix the problem. Booking on another airline would be ideal, but there's definitely some risk they'll cancel the DFW-BHM segment.
Worst case is they close your AA account, forfeiting all miles. Absolute worst case is they come after you for the lost revenue (99.9% unlikely to happen).
Actual worst case is that the DFW-BHM flight crashes and everyone on board dies. I think this is about as likely as either of the alternatives you suggest, and I don't actually think the conditions of carriage allow them to come after you for any lost revenue in this scenario. No one has ever reported either of these things happening based on a single change like this.
But to maybe start over and simplify the problem: looking a couple of weeks out, SAN-DFW-BHM fares are only about $30 more than DFW-BHM fares. Is it really worth any risk of a problem since all of these seem like totally reasonable fares to charge to the client in the first place.