Yes, it is, if he's under 18. Check any and all airline websites that you like, *and* TSA -- children are not required to present ID for domestic flights. (Unless they are lap-children under 2, in which case the airline might require it to prove that they are eligible to fly without a paid-for seat.) The boy in the story is still a child, and all he would have had to do was say so.

TSA: "If you have a paper ticket for a domestic flight, passengers age 18 and over must present one form of photo identification issued by ..."

Add to this that he was travelling with a chaperoned group from an inner-city NYC high school -- the odds are pretty fair that none of the kids in that group have a drivers license or passport.