Have you ever been to India? Not a criticism, I'm just saying.

In my experience, you need to present identification and proof you are flying - BEFORE you enter the terminal building (to check in, though first one has their baggage x-rayed prior to getting to the ticket counters) - in many Indian airports (e.g. Indira Gandhi International in Delhi ). It sounds like Chennai (Madras) may be merely following other Indian airports in this restriction.

By the way, the U. S. Constitution is not anything of particular interest in India. As Hvr says, India bases much of its laws on - the Constitution of India.