They do have a point. If this had been done to Chinese or Russian diplomats, the response from these countries would have been immediate and pretty severe, making headlines around the world. We know all about the Chinese government sponsored riots to express anger. Compared to that India's response has been quite calm and measured.
These sort of problems have festered for a while now. Couple of years ago the Indian ambassador to the U.S. was subjected to an extensive search in one of the airports here. Prior to that the Indian defense minister was searched at an airport.
India feels that the treatment it receives is not the same respect that other countries get. Recently there was the incident of the Saudi princess keeping near slaves and she was let go, and then the Russian diplomats engaged in some fraud, and those guys were also not arrested.
India feels that it is perceived as a "soft state" that does not retaliate or reciprocate for these incidents, that is why they are ignored when they complain.
The sad part is that the U.S. diplomats in India are the ones who have to deal with the consequences, not Bharara or anyone else.
I get it, and they appear to be right about what in the grand scheme of things is a completely inconsequential matter, but there are bigger things afoot. It's too bad no one's politics seems to allow for seeing it.