The bag's dimensions include wheels and handles. The only reason this bag was too large was that it was too large. Why it got too large was a purchasing choice made by OP's family member. This is true on all carriers. For what it is worth, AA has started rigidly enforcing its dimension policy for carry-on and it is a great thing.

Indeed the GA follows his employer's rules, as he should, and those rules are translated into easy-to-understand dimensions published on the F9 website and reflected in its sizer boxes.