It happens on the BA side as well. I got to MIA VERY early for MIA-MAD, expecting a ticketing nightmare which actually took 20 minutes to complete. So, not exactly impressed with the MIA FL I decided to check out the BA Terraces lounge. The receptionist ABSOLUTELY did not want to let me in. Her comment upon seeing my ticket and EXP card was, "Are you flying BA today? I can't find your ticket/boarding pass... sorry but you'll need to go to the AA lounge, this is for BA passengers only."
When I explained the benefit we all know so well she sighed, pulled out the plastic OneWorld cards, and looked through them while telephoning a supervisor. I saw the tier/status rules on the back of the last page and pointed it out to her, she turned it over to find exactly what I'd told her was true, but STILL made me wait while she checked

. Eventually she waved me over to the right hand side entrance. The entrance to the left was closed and rather dark. I got the impression that it was the F lounge but only the J lounge was open at the moment and she didn't want to bother opening the other side for a 'lowly' AA passenger. For the record, I much preferred the BA lounge to even the AA FL.