A license is not an act, record, or judicial proceeding, and so is not required to be recognized.
Since the Constitution forbids states from making agreements with each other (Article 1, section 10) without the consent of Congress, it required an act of Congress for the national driver's license compact to exist. Note that said Compact does a lot more than provide license reciprocity. There's data sharing, so tickets in one state still get you points on your license in your state.
Technically, unless Congress has formally consented concealed carry reciprocity agreements between states are unconstitutional. Unilateral reciprocity ("we recognize all out of state permits" or "we recognize yours if you recognize ours") would probably be ok, since it doesn't require an agreement with the other state.
