Its been a long time I visited this thread. Just wanted to let you all know - I have been hired at another bank. My new boss has been awesome and supportive.
We actually got off on the wrong foot. I was a bit exasperated(looking for job for 5mths) with the kind of response I got from the "desi" MNCs. So my first line out of the door was - "I have stammering so if that is an issue or you want to take a courtesy 10-15 mins interview, please don't waste my time or your time".
After my final confirmation he called me to congratulate and have a word. He said he was a bit taken aback by my candor - specially the "wasting time" part. He asked me not to feel bad about stammering; I had to tell him the scenario mentioned in the thread. He agreed on people/HR feeling too smart and thinking they can read body language/speech and what not. There was nothing wrong in people knowing what they lack and working towards it. I was even specifically told in case anyone from the team or even the company doesn't understand the "equal opportunity" aspect; an official complain can be lodged against the person.