This Flight Attendant probably already got in trouble for violating a FAA regulation. The seat was purchased and legally, she shouldn't have been asked this. Some reseating might have been necessary but they can't not accept a seat if the car seat is FAA approved and a ticket has been purchased for the child.

Always ask to speak to the Purser or "First" Flight Attendant (how some airlines call them). The risk is that you might be encountering someone new or simply doesn't know the rules well. I like Erasmus's technique of not taking your seat and getting the ground agents involved.

I did once switch a car seat to forward facing during the flight itself, to avoid this situation. I believe that this passenger brought an infant seat so not possible.

I personally loved seeing car seats on board. I knew those kids would sleep better and be less of a bother for those around them. I had a lot of military families on my flights so we were used to babies in car seats.