I didn't read what happened but it sounds like a very similar situation I had last year.
I booked tickets with AA for my family, including a seat for my 3 year old. We ended up finding someone to babysit, so decided it'd be better to leave him home. We still needed to bring my infant and I figured maybe we can still use the seat we already paid for. So I checked-in online for my son and boarded the plane with the car seat. If there would be any trouble I wasn't gonna fight. They end up calling my name through the loudspeaker and asked me about my son, they noticed that he never boarded the plane. I said he couldn't make it but I'd like to use the seat for my lap infant. AA was okay with it. Both ways. Maybe if they had passengers on standby (I don't remember if there was) they would have forced me out of the seat. But it was very nice that they could work it out without trying to follow some stupid rules.