It's not the singular they that's flustering: it's when people think they can turn all 'he's into 'they's. You can't do that: singular they works only when number is uncertain, and fails horribly when it is known to be 1. (e.g. you cannot make 'he was a world-record high-jumper' use singular they). In practice, this is not often important when desexing examples. I'm just being pedantic. Again.