Did it vex you mightily that the Sting lyric followed the singular "somebody" with the the plural "them"? Were you taught that "if you love somebody, set him or her free" or "if you love some people, set them free" would be the preferred usage?
Well, rest your battle-wearied head, because Geoffrey Pullum at Language Log says it's OK. No less an authority than The Cambridge Grammar of the English Language takes the stance that they can follow a singular antecedent. Pullum writes, "It's a position that couldn't really be doubted by anyone who had devoted even a few minutes to looking at the facts of usage, be it literary (over the past 600 years) or everyday conversational. Excellent advice."
Pullum scorns the "American backwardness" of "Strunk and White, and their thousands of latter-day co-religionists such as Stanley Fish and the style guides of the Modern Language Association and the American Psychological Association. Why do these sources continue to damn singular antecedents for they in defiance of all the evidence of its constant use by respectable authors during at least the past six centuries? I have no idea."
I can accept the singular they, Sting or no Sting. But what I still vehemently deplore is the misguided use of the subjective I where an objective me belongs, as in the Bodeans song, "Good Things": "No, no, no, don't pass me over. No, no, no, don't pass me by. See I can see good things for you and I." I like the song, but I have no choice but to edit while singing along, making "for you and me" rhyme with "see I can see." (The Bodeans should have thought of that themselves.) And don't get me started on "just between you and I," okay?