Because there could be a statistical correlation with inability to guarantee that this passenger is "known" enough. The point is that he has the right to travel. He does NOT have the right to be in the Global Entry program--that is a privilege. If you cannot meet certain thresholds of confidence in your "known" status as a "good" traveler, then you don't get in. The GE program is about getting the creme of the crop. Being arrested--even if not convicted--could mean that the government cannot be fully confident in you and will not grant you security waivers.