Also, none of this has anything to do with paying for a First Class seat.
If you sat in First, and received the benefits of First during your flight, then you received what you paid for.

People at the airports do not really pay attention to the cabin in which you are seated, unless you're flying TPAC/TATL and in Polaris First. And then, only if you're using the relevant check-in desks for that class of service.