Can India afford to get prickly with big foreign companies? This is the question raised by the ruling Bharatiya Janata Party’s frosty welcome to Amazon founder Jeff Bezos last week.

During his visit, Mr. Bezos laid on the charm. He dressed in colorful Indian outfits, paid tribute to Mahatma Gandhi at his memorial, addressed thousands of small- and midsize-business owners in a stadium, and chatted with Bollywood celebrities. The world’s richest man declared that the “21st century is going to be the Indian century.” He pledged...