<<and dispatched the poor controller to go and make it so for him ....>>
Dear oh dear.. I wonder what planet some people are on!! The "poor controller" would not have done much (except fall about laughing) - allocation of priority categories is nothing to do with him. For priority flights the Flight Progress Strip will be annotated with the category before the controller at the sharp end receives it. If there is nothing on the strip the controller may query it with the supervisor but he certainly can do nothing to "make it so". A biz jet does not qualify for such status unless a) it is carrying a VIP and b) the priority has been agreed well in advance with departments outside of ATC.
As decribed above, certain police and other security flights are Cat B and sometimes Cat A but ATC is well aware of them in advance.