What makes you think Free Basics is doing anything about electricity or connectivity? It is just zero-rating for Facebook & partner apps, riding on top of infrastructure and services built by existing telecom networks in the country with the "extremely corrupt" and "failed" government.
Why the scare quotes around "extremely corrupt"? Do you really think otherwise? India is notorious for pervasive total corruption from top to bottom.
Facebook is not doing anything about electricity; I mention that statistic to demonstrate how modern infrastructure has failed to reach a huge portion of Indians. Facebook has come up with a business model that can reach people that don't have the ability to pay out of pocket for ANY connectivity. By making it profitable for telecoms to serve these people, Free Basics would encourage that infrastructure to expand to the one billion people it hasn't reached.
I'm quoting your phrases to contrast that the fact that, notwithstanding governmental failure and corruption, the reason Facebook can do this at all is because the spread of mobile phones and internet access in India has been a major success story. There are about 900 million mobile connections, and internet adoption is accelerating, with nearly 100 million users added in an year (this is close a third of the total internet user base, so we're talking double-digit growth over 20%.)
Facebook has not come up with a business model that makes it profitable for telecoms to serve people. They've just used their negotiating power, PR resources, government and corporate lobbying to convince telecoms to zero-rate Free Basics, calling it philanthropy.