I have argued with the SC and Amex about the wording of Amex's policy. The way I read that is a 2-year old can access for free and they begin charging once the child turns 3. My 26 month old children were denied access; I did not argue too much since that is consistent with DL's lap infant policy and everything else I could find on delta.dumb.

Edited to add full language from that section:

1. Children 2 years old or younger can accompany you at no charge. Children between 3 years old and 20 years old can benefit from the exclusive per-visit rate of $29 per person.