I think the Navajo Nation may be bigger than you think it is. The two or three major highways that cut across it don't really give you a sense of the size. But that wasn't really my point...
Whether its the Navajo or some other reservation, the difference in forestry management philosophy is evident the instant you pass a sign saying "Now Entering _____ Reservation". You can see the difference with the naked eye. Historically, wildfires that occur on the reservation(s) consume less acres and are extinguished more quickly than those that occur on federally managed land, with the exact same climate conditions in play. That was my point.
Contrary to what Hollywood would have you believe, Arizona has tens of thousands of square miles of forest, the majority of which don't have major highways cutting across them, which is probably why you haven't seen them. The largest stand of Ponderosa Pine in the world is in Arizona. There's more going on than poisonous snakes and cactus plants. But once again, not the point I was trying to make...
The key takeaway here is this; If you manage your forests properly as Col.Jack.Ripper suggests, you will have less wildfires, and the ones you do have will be easier to control and extinguish. Local temperature averages, relative humidity, and annual rainfall notwithstanding. California's wildfire problem is principally caused by ill-considered, political environmentalism, not hot dry air.