Yes, I believe that women should be allowed to lie to men to get them to take care of other men's children. I mean this in the sense that while I think that in many circumstances it's morally wrong, they shouldn't be jailed for it.
I also believe that the government should force child support payments if, as in this case, he'd already taken care of them for 16 years. Personally, I'm not so hot about genes. Many people adopt and do just fine. I also strongly believe that the most important thing is not the genes, but the memes, a term that Richard Dawkins' coined- that is, ideas passed along from one human being to another.
While I believe that there are some advantages if the children one raises look like you, I find children in general to be a joy and would love to have some even if they weren't biologically mine (it'll almost definitely have to wait until I can find a job and a woman I love in 'that way'). Yes, I'm aware that perhaps I feel this way because I haven't actually had any. But I think it's clear that my parents are quite happy with the fact that they had 4 children despite all the arguments us children have had with them and I believe it'd be the same with me.