Here's a related but unusual situation that happened to me yesterday: I have an expensive item listed at fair eBay market value for this item. I received an offer for just about exactly HALF of the BIN price, and at first I was all , but I just declined and wrote something as nice as possible in the comment section. A few minutes later I got an email from that person saying that she hoped I wasn't offended by her offer, but it was all she could spend and she figured she'd take a chance. And ya know what? She was so nice about it and polite that even though I will not sell her or anyone else the item at a huge loss I did recommend another seller who does sometimes sell similar items in her price range.
So, I guess the moral of my story is that occasionally people are not actually trying to infuriate us with these offers. She just knew what she could spend, and figured it was worth a shot. I have to say, I respect that because at least she knows her financial limits and isn't risking her financial health over what is, at the end of the day, an optional luxury item.