Maybe it is time to start to question VISA/MC/AMEX about their policies regarding the acceptance of credit cards worldwide - independently of the home location of the card holder.
Second alternative has been mentioned a number of times - where an alternative billing address is able to be added. Perhaps c/o AMEX Johannesburg would be acceptable to both the holder and AMEX - though perhaps not to AA.
Final question - what would AA do if they were told VISA/MC/AMEX would no longer work with them unless they accepted cards no matter where the billing address was located.
Happy wandering
Fred