Yes, it would be a different control.
As explanation in fig. 6-17 says that two parallel lines creating the tolerance zone are parallel to A and oriented radially from datum axis B, it is the datum axis B from which tolerance zones for all radial elements emanate. If there was no B referenced in parallelism FCF, one would not know at which axis of the part all the tolerance zones meet. Is it at the axis of smaller diameter? Or of the bigger one? Now if you consider that both diameters will always have a certain coaxiality error, it is quite easy to imagine that depending on the datum axis referenced in the FCF, "the origin" of parallelism tolerance zones will differ, so the inspection results may be different accordingly.
Side question: the title of fig. 6-17 is: "Specifying Peprendicularity for a Radial Element of a Surface". Since the figure focuses on Parallelism, is it a typo or is there a hidden logic behind it? Thanks.