From what I could tell, the links you posted are no evidence to the contrary.

First, child abuse is beyond what most would call "parenting"; that term is mostly applied to things like strictness with respect to school homework, video games, pressure to choose certain careers, etc. My argument was that those of us that care about giving their children the best should not sweat too much over where precisely to draw the lines, because the effect of these decisions on the child's personality and life outcome is minimal.

Second, it is very possible that the same genes that increase the chance of a person being a child abuser also increase the chance of their child being, say, an alcoholic or criminal.