Generally, no. A child safety seat is supposed to be installed in such a way that it does not block anyone's exit from the row of seats. Usually that means the window, or if the window seat is vacant, it could go in the middle. But the lady purchased 3 seats, which suggests there were 3 in the party and all 3 seats would be occupied.

Personally I'd have told the FA that the paying passenger in the safety seat was entitled to use his seat as provided for in FAA regulations, and if she wanted to argue I'd ask her to a) contact her supervisor either on the plane or on the ground and if she still pushed the issue, I'd have pushed right back up to the point of LE meeting the plane on the ground and letting her explain her issue to them.

A bit of history: my kid started flying at 4 months and always flew in his own safety seat until the age 5 when he outgrew the safety seat specs. I learned early on to carry a copy of the airline's own rules as well as the FAA rules because a whole lot of FA's hate the sight of a safety seat and will do a whole lot to try to force you to gate check it instead of installing it on the plane. AA was the absolute worst about the safety seat.