Bizarre experience at LAX this morning. Checked in for paid domestic F flight, bags are a few lbs overweight which the agent doesn't worry about (appropriately), but our bags were not priority tagged. We asked the agent why not, and she said it was because we were GLD, not PLT or higher. I let her know that it shouldn't matter because we were in first class, but she pointed to the claim checks that did not have the "P" printed on them. This is literally the first time this has happened to us. Anyone know why? Anything similar happen to anyone else? I'm going to write in to AA about this. Not sure what they'll do if they even care, but aa.com clearly lists priority baggage as a benefit for first/business customers.