If your situation that you've described is indeed corect, it theoretically sounds OK to me. I would check the code to see if there's a definition section which elaborates on the term "dedicated". At any rate, it sounds "uniquely legitimate." If you're getting permits pulled, etc., you have a legitimate argument and may want the AHJ's approval for your alternative interpretation or the requirements.
You'll of course have to check that the fan is capable of providing the minimum amount of exhaust required at the most demanding space. If it's a constant speed fan, the area that's farther away will have a presumably larger static pressure drop in it's duct system, so the airflow for the "closer" space may be greater than that of the "farther space, unless you compensate with volume dampers or duct sizing methods.