Absolutely ridiculous.

This topic comes up here on flyertalk from time to time. There is even a contingent here who feel that someone who only has a personal item (no large item) should be obliged to put it under the seat, so as to be courteous to the other passengers... many of whom bring their massively oversized carryons AND oversized "personal items"... both of which they jam in the overhead.

For the FA to push this when you clearly could not use the underseat storage is outrageous. The later arriving passenger should definitely be the one to check a bag.