Smartest people work in Immigration , Custom and Most revenue generating government offices. Even a simple work will be twisted and harassed for " Chiya Pani" it is like" gas station" making extra money.
Without proper Document and proper stamp on it will be impossible to leave the TIA. You need to show visa or document fly your Destination. If you have kept your green card ( not tossed after Oath) and still has the valid date, you can show that. What are you going to say on US custom ? You can tell that they did not stamp on US passport.