Not a lawyer, but it seems pretty clear to me (if the Constitution still holds any sway):
Article IV
Section 1.
Full faith and credit shall be given in each state to the public acts, records, and judicial proceedings of every other state. And the Congress may by general laws prescribe the manner in which such acts, records, and proceedings shall be proved, and the effect thereof.
Section 2.
The citizens of each state shall be entitled to all privileges and immunities of citizens in the several states.
It seems pretty clear to me as well, but you are welcome to test your theory in court.
I'm not willing.
There are exceptions. In Kansas a 14 year old can get a learners permit and a 15 year old can get a restricted license. Try driving on those in Missouri and you’ll get a ticket.