"They" can be singular or plural. It can easily refer to a single entity that is gender ambiguous (like a company, team, etc)

People say that, but it is grammatically incorrect.

A few examples of the singular "they", courtesy of Wikipedia:

Eche of theym sholde ... make theymselfe redy. — Caxton, Sonnes of Aymon (c. 1489)

Arise; one knocks. / ... / Hark, how they knock! — Shakespeare, Romeo and Juliet (c. 1595)

'Tis meet that some more audience than a mother, since nature makes them partial, should o'erhear the speech. — Shakespeare, Hamlet

I would have everybody marry if they can do it properly. — Austen, Mansfield Park (1814)

That's always your way, Maim—always sailing in to help somebody before they're hurt. — Mark Twain, Adventures of Huckleberry Finn (1884)

Caesar: "No, Cleopatra. No man goes to battle to be killed." / Cleopatra: "But they do get killed". — Shaw, Caesar and Cleopatra (1901)

The singular "they" has extensive precedent. Some proscriptive grammarians feel that it should be disallowed, but given the usefulness of a neutral pronoun and the venerable history of the usage, I think they may be safely ignored.

I think that is a little bit misleading; I am fairly certain that there are plenty of examples of nonstandard usage in works by any of those authors that you would absolutely not accept as correct. Particularly Shakespeare, who is well known for using common parlance in his works rather than proper English.

"Did you talk to the person from the cable company?"

"Yes, they told me to file a complaint with corporate."

I'm not sure how that's grammatically incorrect.

That actually is grammatically incorrect in English even though it is used often in common parlance; they is supposed to only be plural. The correct usage would be "he or she" if you don't know the gender of someone; the reason why "they" is used so commonly for singular is because of how unwieldy it is to say "So about your friend; does he or she bring his or her ipod on his or her way to work?"

It's actually a huge flaw in English, and there has been tons of proposals of gender-indifferent singular pronouns like "xe". On the other hand, "you" used to only be plural and apply if you were talking to a group of people ("thee" was singular) and obviously the correct term today is you for both singular and plural.

It's easily possible that within the next 50 years it will be commonly accepted to use "they" as a singular pronoun in formal communication, but its not today. You would almost certainly be marked down for using it in that manner on the SAT or GRE for example.

Very true. I do the exact same thing. Language is a beautiful thing.