The father "propagating his like" and all that does matter in some cultures though. And it's not just a matter of shame, which can be considerable, for the parents. Bastardy can carry a stigma for the child as well that may even persist into adulthood.
I'm not endorsing such beliefs, mind you. Nor am I accusing these parents of holding them. Hell, I neither have nor want kids, for that matter. But the cultural attitudes I described do exist in the world. And they can cause significant problems for the child beyond the, not at all insignificant, medical questions that may arise from unknown parentage.