Sure, I understand the distinction you make, but the point you highlight is exactly my point.

State A may permit anyone to carry concealed for example.
State B may permit only people born on a Tuesday to carry concealed.

This law would effectively make State B permit anyone to carry concealed, because they would recognize any permits from State A and anyone in State A can get a permit to carry concealed. Thus it would effectively override completely their own legislation regarding permits for anyone travelling through who has a permit from any one of the 49 other states.