Hi!
Most HVAC guys want at least 1" space between the door and the floor, if there is no return provided! Depending on the size of the room, size of the vent and the airpresure fron the fan, there can be an appreciable pressure build up in the room. Add the new carpet and pad, he could end up with a very small crack under the door. If they added strip between carpets, More space is gone! If the room is close to the air-handler, the pressure will be higher and if the other rooms have the same problem, it all adds up!
Best,
Clammer