She may be technically right - not sure how it is in the US, but in many EU countries you can’t film a private person without their consent, even in public spaces. She is not a public official (cop, public administration, politician, etc.) on duty where the rules are more tolerant, she is an employee of a private company. The privacy protections can sometimes go to ridiculous extents.
However, the same goes for people with smartphones being asses and filming where they shouldn’t. Shoving a camera in someone’s face is a sure fire way how to escalate a misunderstanding into an open conflict, regardless of who is “right” - especially after that guy admitted that he arrived with baggage that was purposely over the weight limit. That is a great way to slow down the queue at the check-in counter while the bag gets handled and paid for, even without someone having an argument with the clerk. People queuing behind this guy certainly “loved” him for this - someone was again trying to be smart and flaunt the published rules. Sadly a lot of people think that this is OK and not at all selfish.
That said, you are completely right that she is being a dick to the customer and should be fired. These clerks should be sufficiently thick skinned and trained to deal even with annoying customers without blowing the gasket like this.
