It's true that some states only recognize permits held by other states by residents of those states. Colorado is being sued over this - oral arguments in a federal circuit court appeal in the Peterson case are happening on the 19th of this month.
Gray Peterson is a WA state resident with both that and a Utah permit. CO recognizes UT permits but only by UT residents. Worse, the city of Denver refuses to recognize open carry so Peterson has no legal carry recourse at all in Denver.