Similar here. I did not try to carry, but we had a convertible in the car, no infant seat. They did not want to leave with the baby in our arms. They apparently had to see the baby strapped in the seat while leaving the maternity unit on 2nd floor.
: So DH had to get the seat out of the car, bring it to the room, we put baby in, walked out like that... Got her out, seat went in the car... then baby went in. The thing is that they have no idea if your seat is properly installed, just that the baby is in it.
Next time, I would just borrow someone's infant seat, get the baby out of the maternity unit like that, they will never know that she is going in a different seat.
My husband did rub it in and asked the nurse what would happen if someone was to take public transit to get the baby home, so no car seat. She was quite puzzled about it...