they not only can have a morphosyntactically (and semantically) singular antecedent, but it can do so even if the gender of the referent is known, and syntactically overtAnd
This use of they isn't ungrammatical, it isn't a mistake, it's a feature of ordinary English syntax that for some reason attracts the ire of particularly puristic pusillanimous pontificators, and we don't buy what they're selling.Heh.