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.

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

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