The optimal play and the "rational" play are two different things. I've already stated that I would be very unlikely to offer a low offer to my opponent, mainly because I figure he'll be an idiot and overvalue spite.
And being an "idiot" this player will come out way, way better off than otherwise. Doesn't sound very idiotic to me.
Any idiot chooser would never come out ahead. He'll reject some offers. Only if the negotiator knows this is he in trouble.
Of course, having an idiot negotiator or coming across as someone who won't accept a low deal would have you come out ahead as well.