"I have the impression that English is the, er, Linga Franca of the educated classes in India. Surely the kid learned English over there before coming here."

True (most of the times.)

An interesting phenomenon occurs due to India having a large number of disparate regional languages. A South Indian, for example, may be able to communicate with a North Indian more comfortably (or at times, only) in English... 'Coz the only other language they know well is their respective regional language, which may or may not be Hindi. I experienced this first-hand, and the strangeness and humor of the situation was brought home only when an American noticed it.

Edit: Having said that, an Indian still has to learn English, as it is not his/her 'mother-tongue'. Many are not as comfortable with spoken English as they are with reading or writing it; and their use of the language, while being correct on most occasions, might be considered awkward by native speakers of English (another first-hand experience!)