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.
Related on OB: Lying to Kids The Third Alternative
My wife and I are planning to have kids, so of course we've been going through the usual sorts of debates regarding upbringing. We wondered briefly, will we raise our children as atheists? It's kindof a cruel experiment, as folks tend to use their own experiences to guide raising children, and both of us were raised Catholic. Nonetheless, it was fairly well settled after about 5 minutes of dialogue that atheist was the way to go.
Then we had the related discussion of whether to teach our children about Santa Claus. After hours of debate, we decided we'd both have to think on the question some more. It's still been an open question for years now.
Should we teach kids that Santa Claus exists? This isn't a new question, by any means. But it's now motivated by this thread about rationalist origin stories. Note that many of the posters mark the 'rationalist awakening' as the time they realized God doesn't exist. The shock that everybody, including their parents, were wrong and/or lying to them was enough to motivate them to pursue rationality and truth.
If those same children were never taught about God, Santa Claus, and other falsehoods, would they have become rationalists, or would they have contented themselves with playing better video games? If the child never realized there's no Santa Claus, would we have a reason to say, "You're growing up and I'm proud of you"?