TKD is a great program for the kids, my son is a Black Belt in TKD and a 4-time state champion. However, based on time requirements I don't see how they could be 3rd Dan Black Belt. They shouldn't even reach 1st Dan Black Belt for 5-6 years, then there are minimum time requirements between each black belt level. Starting at age 5, a person should reach 3rd Dan Black Belt between 15 and 17 years old.
As I am sure you know, there are numerous different Taekwondo associations, federations, and alliances, both domestically and internationally. The various time and class attendance requirements between belts are governed by the guidelines adopted/enforced by the particular organization with which the student is affiliated.