Okay, maybe this is a stupid question, but here goes...
I see all these discussions saying that most states will not license people who were not on-campus students (i.e. "ELP" students). My question is: How do they know that you didn't go to the campus? Does it say on your transcript or what?

They probably know the reputation of IUHS. I read somewhere eariler on valueMD that people have been asked for proof of stay on the island, like your passport, travel stubs, receipts, etc.