The thing is, at every turn there was just a coincidental reason something happened to turn out that way. If you don't think this looks highly suspicious on someone whose hands and bag seems to keep setting off explosive detectors, i don't know what to tell you.
If they aren't supposed to target the people with odd stories who set off explosive detectors, who exactly are they supposed to be targeting?
- "My name is ___" (ID)
- "Until two days ago I lived at NYU" (NYU ID)
- "Previously, I lived at $address" (ID)
Thousands of people in the U.S. fly without business cards or ID listing their current addresses. University students are just one obvious example. This simply isn't uncommon. If you want to target that, you might as well target retirees or snowbirds. Of course, you wouldn't, since you profile based on demographics, ethnicity, etc, in addition to merely not having a current piece of ID or a work phone number.
Explosive detector results, sure. So determine it was a false positive and let them go. It doesn't take 3.5 hours to verify a person and their bag don't have any actual explosives on them. The amount of questioning was not warranted.