Just because something is written down, it doesn't mean it is correct. Mistakes happen, people lie, or they tell what they think is right but it isn't.
I've found errors/lies on gravestones, bmd certs, parish registers, Wills, you name it!
On the plus side, my illegitimate gt grandmother's marriage cert gives her mother's name in place of the father so at least one of her parents was acknowledge. Let's face it, mother's are a bit more involved in the birth of a child anyway!