JRH is mostly talking about the long term. Parents have little effect on their children's adult beliefs and behavior. They have an enormous impact on what they believe and how they act as children. One of JRH's examples that she brings out several times is what language is spoken fluently as an adult. We tend to assume kids get it from their parents, but that's a spurious correlation. Nearly all normal children are exposed to parents and peers who speak the same language, and the children end up matching both. When parents and peers speak different languages, children end up speaking the same language as their peers, once they move out of the home. While still at home, they continue speaking to their parents in their parents' language.

Similarly, the Santa question is about what your child believes during the formative years. No one continues to believe the Santa story beyond 15, so that isn't a question of peers vs. parents.