All they've ever done for me is look at the child and pull out a generic child badge, then register the child's name and an emergency phone number in the system (connected to the parent's badge).
Alyssa, if they do look up the child in the system and find a member ID, that member ID will ALSO have the child's birth month/year, which if anything only 'proves' your case that a child badge is deserved for 2012.