No matter what you think your chat offered, iPhone warranty is NOT, nor has it EVER been international. A phone purchased in the US CANNOT be replaced in India. If an iPhone requires being replaced, Apple will ONLY replace a phone with the exact same model as was purchased. US phones are different from phones sold in India as Apple sells iPhone based on country of purchase. Since you could never get a US model as a replacement in India, this means you will need to travel back to the US with your phone for warranty replacement.
Whether you want to believe us or not, doesn't matter. India resellers are notorious for refusing warranty service on a phone not purchased in India.
Buyer beware. Your money, do as you want. Just know there are very probable issues buying a US iPhone and expecting or getting warranty support in India.