Little over a decade ago, I was departing DEL for NYC ad=nd my passport had a very old picture of mine which looked a little like me.
The immigration agent refused to believe it was mine (even though I had my NYS
Drivers license... I suppose he was looking to get paid or something)
After 10 minutes of arguing... supervisors involved.. etc.. etc..
I said.. "look.. I dont have any cash..
I'm not paying anything and I'm not moving anywhere unless
you stamp my passport and let me go."
A couple of minutes later I was on my way to catch the flight

I had a similar experience once ex-BOM, out of the many times I've gone through there. My passport picture at the time had been taken when I was 15 and I was about 22 at the time. The immigration agent refused to believe it was me even though I showed him other current photo id. Finally, he said "wait here", went off to another counter, came back with a torch and shone it on my neck (my passport said I had a little black birthmark to the left of my Adam's apple, something I'd never noticed before - guess my dad put it there when he applied for my passport). Satisfied, he then stamped my passport and sent me on my way.