I'd think a parent would be aware of physical intersexuality

This is not reliably true. I have a friend who is a genetic chimera (fraternal twins, fused early enough in development to turn into one basically normal-shaped person). She was considered anatomically male and normal at birth and well past, and didn't find out she had female organs too until her twenties, when they finally did an ultrasound to track down her irregular abdominal cramping, then did genetic tests to explain why there was a uterus in there. This gave her a relatively socially acceptable excuse to assume a female social role.