Top "flight " coaches, do not restrict themselves to any particular group ( unless, under contract ).
The major difference between the A/M and Freds syl.wise , lies in the Bronze syl.; but, essentially the same with the odd "twist " .
As to Freds or A/M competing in outside events, allow me to give you some background.
On several occasions ( 2 in particular... Phoenix and NYC ) I was the organiser of 2 NDCA recognised events, in which both had participants Prof. and Pro .Am.
In matter of fact, in one of those, an A/M teacher, danced with a F/A teacher in a Prof comp. ( that was in 1974 ) and the NYC one ( in 1964 ) had, again, both chains in attendance .
That( NYC ) was the 1st major comp. that both Larry and Betty Silvers and Joe and Nancy Jenkins competed. I shortly afterwards , coached both, before they and I moved on ( them to much greater fame), to other locales.
PS... Not all chain school owners, are open to such outside activities .