I agree that the press coverage is (and always tends to be) a bit whacked when it comes to Wikipedia, Wikimedia and India. And it doesn't help that the explanation is pretty clear but complicated. In a few months, we will have the Wikimedia Foundation India office, the Wikimedia India chapter, and of course - as always - the Wikimedia community in India, not to mention various sub-community groupings. I can only see more confusion unfortunately.
Perhaps you can set up something on India-meta? An explanation such as the one just offered (who does what) + something about the difference between Wikipedia and other Wikimedia projects would be very useful for the press, if kept simple. Then we could point them to this page every time there's interest - or print it out and distribute it for subsequent press interactions as well. I'll help, and others will too - I'm sure - if you get it going.