No, that's Borges alright. (He's one of my favorite authors, so I've read all his fictions many times. I don't have my books handy to say exactly what story it is, but I'm fairly sure it's one of the later ones.)

EDIT: I leafed through my Collected Fictions until I found it. It's "The Bribe", in The Book of Sand (Borges's 2nd-to-last collection). Turns out the appointment is not to Oxford, which explains why my googling failed, and is actually who is to chair a literature conference in Wisconsin.