Executive Assistants in customer relations is kind of a department within a department that represent the Leadership Team (ie WW and MB) and therefore have access to a number of systems that can verify a whole range situations (NOMAD, Onboard Tracker, Amadeus, World Tracer, etc).
It's not a case of taking someone's word for it, it's a case of making investigations prior to going to legal. It's taken quite seriously by outstations (in this case DFW) as they can be held accountable in a court law. Most communication with pax is on WW or MB letterhead, therefore the department has to be sure of the facts before approving settlements like the one I mentioned.