You know, I looked at the discussion about this on Flyertalk, where there are a LOT of postings about the subject. It's interesting that the opinions of the posters about the *obvious* age of the child are about 50/50, in terms of believing that said child appeared to be over 2 yrs. old. I've got 2 nephews the same age (11 mos.), one of them weighs 28 lbs., is walking, and stands nearly 3 ft. tall, the other weighs 16 lbs. and is barely crawling. The first child's parents routinely encounter people who are surprised to find that he does not speak, because those people are assuming that he is well over 2 yrs. old. Appearances pretty much mean nothing.
I didn't see the show (I just have broadcast TV) but SWA (and every other airline I've ever dealt with) makes no secret of the fact that a passenger attempting to fly a child as a free lap baby may be asked for proof of the child's age. It is better PR to just ask all the time; regardless of how old the child might appear to be. IME, domestic airlines will ask for proof unless the baby is obviously too young to sit up without help, and any lap baby who can walk will always be 'carded.'
Believe me, there are a LOT of people who will lie about the age of a 2-3 yo to try to avoid paying airfare for that child. Airlines who let passengers get away with lap-carrying a child that age are violating FAA safety regulations. You had better believe that on a televised program they are going to ask.