Although the U.S. government doesn't care how old a skydiver is, the state governments will not allow a parent to sign away the rights of a minor to sue. The USPS requires its member drop zones to only allow skydivers 16 years or older to jump. Now, considering that it's one of the most popular actors on the planet, I'm sure that more than a few drop zones in the U.S. would have easily risked getting sued in exchange for all of the publicity, but Mr. Smith decided to jump at Skydive Dubai instead.
To feel more comfortable with his decision, The Fresh Prince went skydiving a week prior with his old co-star Alfonso Riberio. He also got some wind tunnel time with the Crown Prince of Dubai.