Women can be conniving b*tches, especially when it comes to having kids. Even women who conceive through sperm banks can use dishonest means to obtain information about the donor they chose and try to solicit money from them.
I don't think the guy should have to pay a red cent to this fool woman, and personally I think the woman ought to be taken out behind the nearest building and shot for being so greedy and stupid. The woman probably just talked sweet to the guy and had every intention of burying her claws into his wallet from the start - hell, for all I know, she just wanted to get knocked up so she'd have some free money coming in from the father.
The guy is a little dense for giving in to this woman's request, but the fault lies more on the woman. If I were the guy, I'd be suing her for emotional distress at the very least.