That's another furphy. Sweeping statements like that may have a grain of truth in the finite points of heraldry, but certainly not as a general rule. The father's arms certainly go on the left of the shield as you look at it and his wife's father's shield is depicted on the right. However, when this occurs, the children only get to display their father's arms as heirs to his arms. His wife's arms are actually those of her father which she has been allowed to use for her marriage only.

Unless the wife is an heraldic heiress (i.e., she has no brothers) her (father's) arms are only joined with those of her husband by impalement - the children don't inherit their maternal grandfather's arms unless their mother is an heraldic heiress when, if this is the case, the arms are quartered with the husband's arms in the top left and bottom right and the heraldic heiress' arms in top right and bottom left - the children of such a union are able to display quartered arms.