Pray consider this sentence from one of Rex Stout's Nero Wolfe murder mysteries: "Everyone has something they don't want anyone to see; that is one of the functions of a home, to provide a spot to keep such things."
I offer it not as a response to the specious argument that if you have nothing to hide, you have nothing to fear from the National Security Agency's surveillance,* but rather to consider it as further evidence for singular they. To my mind, it carries more weight than Jane Austen's every body ... they.
The first reason is that it appears in The Red Box, published in 1936. Yes, 1936, when, by gum, children had English grammar pounded relentlessly into their empty little heads, before progressive educators, lexicographers, and linguists betrayed the English language to the barbarians.
The second is that it is uttered by Nero Wolfe himself. The Wolfe mysteries are narrated by Wolfe's assistant, Archie Goodwin, who is relentlessly breezy. ("The etiquette seemed to be turned off, so I let myself out.") But Wolfe always speaks formally, in standard English, and is finicky about grammar and usage. In Gambit, he burns his copy of Webster's Third because it "threatens the integrity of the English language." A solecism would pain him more than horseradish on oysters.
So, if you are of a mind to be persuaded by evidence, you now have one more piece of it.
And if you think you know better than the evidence, well, I have worked with you lot before.
*Of course, it is that. Everyone has something to hide; if you are not embarrassed about something or determined to keep some aspect of your life private, you're probably not human.