You were denied wrongly both times.
I'm QF Platinum and regularly use AA Flagship Checkin at LAX since it's my home airport. Access rules are clearly stated on aa.com. Never have been denied or questioned for my domestic flights. They usually look on their list, not find me on it, and I just tell them I'm Qantas Emerald (yes, I've found that's easier for them than Platinum, Black, Gold, etc) and they let you right through.
Never any problem in Dallas either (though the food in there is nothing spectacular).