I have heard of a situation where the seller rejected out right. When the buyer returned with a higher offer, he (the seller) countered above list price to prove a point. If a seller is not backed into a corner to sale and lets emotions take over, you may close off a deal with one low, insulting offer.
I agree with my colleagues, make an offer with consultation from you agent and in accordance with fair market value. Though low offers may work under certain situations, those situations are the exception, not the norm. And insulting an emotional seller can never set you up for a successful meet in the middle negotiation.