After discussions of the same subject on Twitter and CNN, here's some fascinating history of English grammar in The New York Times: On Language - All-Purpose Pronoun.
The authors, subbing for William Safire, are Patricia T. O’Conner and Stewart Kellerman, who once titled a book “Origins of the Specious: Myths and Misconceptions of the English Language.”
"They," they say, was once acceptable as an indefinite singular pronoun.
The surprise: The authors blame an 18th century feminist grammarian for our abandoning a once-acceptable "they" in sentences like, "We don't know the murderer's identity, but they may strike again." The result was years of misleading (and sexist) use of "he" as a synonym for "he or she."
However, O'Conner and Kellerman say it looks like "they" may be on its way back:
"...so many people now use they in the old singular way that dictionaries and usage guides are taking a critical look at the prohibition against it. R. W. Burchfield, editor of The New Fowler’s Modern English Usage, has written that it’s only a matter of time before this practice becomes standard English: 'The process now seems irreversible.'
"Merriam-Webster’s Collegiate Dictionary (11th ed.) already finds the singular they acceptable 'even in literary and formal contexts,' but the Usage Panel of The American Heritage Dictionary of the English Language (4th ed.) isn’t there yet."
If asked about this by [a student] (students), I probably would tell (them) [her or him] to listen to the sentence and make up (their) [his or her] own mind (minds) about "they" -- or consider rewording everything to avoid jarring people whose ears are tuned to one sound or the other.