I am not a frequent traveller but till date I have not heard about the on arrival visa in India. How cum educated parents like you forget about the Visa knowing that both of your children are US citizens by birth? I won't imagine any other treatment if the incident would have been happen while travelling in reverse direction (from India to US). Do you think after getting the Green Card and staying in US for long time you get previledge entering India without any Visa?
I would like to congradulate the Immegration Officer for their work