I don't remember being told this during my CHL class. So basically, just because a state says it's reciprocal, doesn't mean that the WHOLE state is.
The reservations are not part of the state. They are under the protection of the USA and are considered independent nations. It's an antiquated concept that should be done away with, but political correctness and contract law make it difficult. They are Americans but not Americans. Confusing hey?
I travel in New Mexico, Colorado, Arizona, and Utah a lot, sometimes in the Pacific Northwest. You cannot travel on an interstate in New Mexico with out crossing a reservation somewhere.
To answer you question, I would say that no reservation allows or recognizes a CHL unless you are a member of the tribe and maybe not then. You can ask for permission to carry but considering the way their governments are structured and operated, then throw in a ample supply of contempt for Americans, it is not likely that any outsider would get permission. Think Chicago politics with a Native American face.
It's generally thought (at least in NM) that if you are on major highways tribal police will not bother you unless they want to mess with you for some reason. I lock my carry gun (you can only carry one concealed weapon in NM!) in the trunk or box when I am out in the Navajo res on back roads. I think it is stupid, but so was the restriction on carrying in The National Parks and Monuments. Gun laws do not make logical sense, are politically motivated, and ineffective just about anywhere. Reservations are no exceptions. Just be discrete, stay on major US and state highways and don't do anything to get stopped for.
Wayne in FW