It is BA policy at MIA to refuse entrance to AA customers connecting to domestic flights, even though the oneworld rules would indicate an eligibility for that lounge. They will not bend it at all. You were treated exactly in line with their policy.

They told me that if you are connecting to an international flight, they would let an AA passenger in . . . but if you're on the return leg and connecting to a domestic flight, the answer is a firm "no."