Im not sure that its fair to put the AA agent on the line for this.... most gate agents are poorly trained and have no clue what to do in many "non plain vanilla" situations. To give a very specific data point... my last long haul flights on AA involved a GJT-PHX-MIA-EZE route. At check-in, the agent was super friendly, but 200% clue-less on what he needed to ask me and or look for. He basically asked me if I had experience with this.... I was this guy travelling on an Italian passport and going to Argentina (with no return ticket). By the time he got through to the part of the "cheat sheet" that touched on the Covid certificate, he didnt even ask me to show him anything.
I only got a Candid question.... " do you have all you need to make sure they will let you in when you arrive down there? ".
I said, "yes".... and offered to sign a waiver/affidavit so he could be kept of the hook. He replied " No Need. You seem to know what you are doing !! "