We had a good friend when we lived in
We can mention Heavenly Father, Lehi, Abraham, Isaac, Jacob, Brigham Young, Ezra Taft Benson, Hugh Nibley and lots of other visible leaders as examples of righteous parents who had children rebel - but we also can mention every single one of them as examples of righteous parents whose children generally did not rebel. We can say they prove the proverb incorrect, but we also can say they prove the proverb correct. In my opinion, seven of eight (for my friend) or two out of three (for Heavenly Father) proves the proverb as a general rule.
In the end, it really is up to individual agency, so nobody whose child or children struggle should assume automatically that it was their fault, but proper training as a child can make a huge difference.