I booked a flight on AA's website and I picked seats based on the limited availability online. Obviously there are many seats that show as unavailable but which are available for certain customers. I called and gave my BA Gold Executive Club number. I thought I would have access to the "premium" seats and was surprised to find out that what they could give me was no better than what I saw online.

Is it true? OW Emerald members (like BA Golds) don't have better seat access on AA than John Doe booking his first flight ever?

How does BA handle the opposite? Does an AA top tier member have access to all BA seats in advance like a BA Gold does?