I was basing it on seeing Paki born western cricketers and the "German" Abrar guy being allowed in recently. But I think there was a similar debate on here a few weeks ago, and it seems like your argument was mostly agreed upon.
Having said that, how would the Indian government distinguish between "name and ancestry" of a Pakistani Muslim (especially Muhajir) naturalized US citizen vs. an Indian Muslim naturalized US citizen? And what if the Paki US citizen lies and says he was born in the US?
Can the Indian government even disallow any US citizen a travel visa on the grounds that he was born in Pakistan? Wouldn't that be illegal per US laws?
The Indian government can deny a visa to any foreign national at its discretion. They do not even legally need to give a reason. It'll just say application rejected. US laws have no jurisdiction over our visa policies.
Over the years, the MEA in conjuction with its RAW attaches in foreign embassies (who officially go as IFS officers) have proven to be very effective at identifying any pakistani origin applicant, even if he or she has only partial ancestry. I don't know all their methods, but they do an effective background check of every applicant.
Although I'm not sure about those countries that we have a visa on arrival agreements with. I need to check about how they prevent pakis from coming from there.