Both Hubbell and CdC are totally on Navajo Land as are many sights in AZ, NM and else where in the S/W. Personally I found the Trading Post to be quite a prize and my wife sat and talked with the women in the VC for a couple of hours. I talked with the silversmith that was there the day we visited and it took about a half hour before he began to loosen up and talk to me. I had just read about The Long Walk and the Treaty that Returned the Navajo Ancestral Lands to the Navajo and wanted to learn more about the culture of the people. A very amazing afternoon at Hubbell and with a true Navajo elder who also holds a Doctorate in Sociology.
The bottom of Canyon de Chelly is Sacred Land of The First Nations People and has been designated as such. To them it is as much a church as any structure built by European or African people. The Navajo happen to be the custodians of the land and if you notice that there are no cell towers in Navajo-land nor are there any on the Hopi Reservation. It is not part of their culture and they don't feel the need for our cell and internet systems on the reservations. They do not like nor do they want huge arrays of signs on their Sacred land, but if you approach them politely and with respect, they will teach you many things.
Just remember what the US Army, the 7th Calvary in particular did to them and how they are treated by most non-First Nations People and you will begin to understand why they are the way they are.