I disagree. In the context of this thread, Robert appears to be the PKV. Unless Robert was a passenger in the car while his imaginary friend was driving, he cannot know for certain that his imaginary friend was indeed driving at the material time. What he can know is whether he gave the keys to his imaginary friend, and possibly saw his imaginary friend drive off.
The handing over of the keys (by Robert to his imaginary friend) is relevant insofar as most cars are somewhat difficult to drive without the keys, but beyond that I would suggest that it is irrelevant to the OP's obligation.
If we can assume that the OP is not the PKV, then his obligation, when so required is to provide any information that is in power to give and that might lead to the identification of the driver. If there is a likelihood that this will go south, then it would seem appropriate to ensure that he dots the "i"s and crosses the "t"s.
The information that is in his power to give would appear to be that the vehicle was assigned to Robert (Robert was the PKV), and that Robert has informed him that <name of imaginary friend> was driving at the material time.
However, without seeing the notice, it is not possible to determine what exactly is being asked of the OP - merely to nominate the keeper of the vehicle, or chapter and verse.