Why don't you agree, if the two discussed and reached an agreement? If the mother does not ask for help, why should the man be forced to give it even if it's not what either of them want?
My girlfriend's dad met a woman 10 years his senior when he was like 22, when hiking in the grand canyon. She had sex with him and they went their separate ways. Two years ago he got a call from a woman, she found out through 23 and me that he was her biological father. Turns out this woman was married, and they'd be trying for years to get pregnant and nothing. She went out and found someone to have sex with, told him she was on birth control but wasn't, with the express purpose of getting pregnant, and then she told her kids (she had twins) and her husband that they were his. I realize this is an extreme case, but if it's never okay for a man to not owe support to the woman no matter what, then wouldn't it be unjust for him to owe her, when he was misled and used?
Anyway back to more normal circumstances, I think if two people agree on something, then they should be able to do whatever they want.