My mother got a call about three years ago from a man who told her he thinks his mother is my mother's sister. Turns out my grandmother had a child at 16 and put her up for adoption. Now I have an extra aunt and she's super cool.
There's probably a lot of mothers out there who feel really worried when they read news stories like this and there's probably a lot of people who aren't much like their sibling(s) that wonder.
Darwin spinning in his grave: "Nah, we already have a child, let's not have any more."
The angst they save their family still exists - they'll keep it to themselves. Even without sharing, that's bound to have some social implications.
Could that happen? Or are the DNA tests correct 100% of the time?
Assuming the other parent is human, or even from the same tree of life, that's not going to happen, because the actual parent will share some DNA with the purported parent; you'll never get 50% match the actual mother, 0% match neither the mother nor the putative father.
The father not knowing that the child is not his is a different ball of wax. The mother will always know the child is hers or not (baby switching in hospitals and other rare events excepted). What percentage of children have fathers that are not their biological fathers and the father doen't know it? I have no idea, but this fact being discovered via DNA is going to really hurt a lot of relationships from each discovery.