Most but not all airlines have rules in their official policies that are colloquially called flat tire rules. These rules specify how to accommodate passengers that present themselves too late at the airport. I'm not familiar with AS's rule policy though.

This is not an IRROPS situation where the agent can issue tickets on another airline and give them to the passenger. When airlines do that they do have to pay the other airline for the ticket.

$250 for LAX-SJO sounds like they paid for a new ticket to me. Possibly the AS agent refunded their original ticket using it as credit towards a new ticket?