When the government considers you for Global Entry there are really two separate things they are evaluating. The program makes you a ‘trusted traveler’ and that comes with expedited airport security (less scrutiny, you don’t take off shoes or take out liquids, and don’t have to go through body scanners) and expedited immigration and customs. They want to know that you aren’t a security risk, and also that you’re not likely to violate customs rules.
That can lead to some odd things in your history keeping you out of the program, or getting you kicked out of the program.