It is private property, you have no right to video and the purser’s choice of words was fine. You paid to travel from point A to point B and you did. Your ticket,no matter what the class didn’t include filming rights. ( unless there is fine print I’ve never seen)

BTW, American Courts have upheld that shopping malls, although open to the public ARE PRIVATE and mall owners can allow and disallow actions. I,e, solicitations and religious outreach etc. The only thing they can’t do is keep out an individual based on their background. While not a lawyer, I don’t see a big difference in planes. Private but open to the public.,