Some of them make reference to David Reimer, and - as I've actually read his book - I'm not so sure of the relevance.

I think it's very relevant. They're trying to let the poor kid assert whatever gender and gender expression comes naturally. Just because the kid's probably got gender-identifying genitalia doesn't mean that's the gender identity that the kid would pick for hirself. They're trying not to do accidentally to their kid what was done to Reimer deliberately: force a gender on the kid that's not the kid's. Bully for them.