I'm not a lawyer much less an international one, but "obviously" there's a difference between a fee for expediting a request that is documented officially and one that is not. I think it would be unreasonable to call the former type a bribe. I recall that there is an option in the US to get your passport faster if you pay an extra fee, but it's not a fee that somebody random made up and they collect.

Good news for US businesses doing business in India.