Remaining calm, being polite, and sticking to the facts tends to work better as most upset customers rant about peripheral stuff.
Add to that effective use of the industry lingo, and they know you are not your average kettle. Particularly with airline staff...using terms like "IDB" and "NRSA" and calling the airline by it's two letter code works wonders.
I once thwarted a non-rev seat poacher who had the support of her FA buddy by saying something along the lines of "Come on, you know the UA rules on NRSA's and displacing rev pax, and if I VDB myself I will tell the station sup that you two ladies will take the late". They moved damn quick while apologizing and I got a free drink from the FA who was terrified I would make trouble for her.
I did anyhow.