Bob Ladd just got a message requesting an academic reference letter for someone who I will refer to as Gerald Black. I am concealing his name, but not his gender: he is male, and his real name couldn't leave you in any doubt about that. Further concealing the identity of the innocent, let me say that he is applying for a job at a university that I will refer to as the University of Penzance (there isn't one), in the Department of Criminology (that isn't the real field; all of this secrecy is beside the point, but you will see the point in a minute). The message begins:
Dr Gerald Black has applied for a position of Lecturer in the Department of Criminology at the University of Penzance. I would be grateful if you could provide a reference on their suitability for this post.
Startling, didn't you think? My claim has always been that you just can't get singular they with a proper name of a person as antecedent. And now, here is an example of it. If you think the letter is unremarkable and fully acceptable English, then we have a counterexample to my claim. On the other hand, if you find their the second sentence jarringly inappropriate, the sentence is just evidence that I'm right. You be the judge.
I happen to think the use of their sucks canal water, so I'm still happy with my claim (though I did once come close to thinking I had found a counterexample myself: see here).
But then that's just what I would say, isn't it? You can't really trust me once I've stated my generalization and hitched some of my street cred as a grammarian to it. What you've got to decide is whether the evidence you see and hear convinces you that my generalization simply has to be discarded. If so, tough for me: I'll just have to get used to the fact that I was once (just once) someone who was wrong on the Internet.