I watched that as it happened- here -in Tucson- of course! The provenance should be fairly easy to find.
Kit Carson's life-especially the part of his govt career in relation to the Navajo Nation- is well documented and a Kit Carson special will be on PBS soon. An Anglo family living in those parts -and farming up there- has a high likelihood of being Mormon. and no group loves to document everything to do with their history and ancestors as much as Mormons. There was a very good reason they brought that blanket in instead of jewelry, baskets or pots, though I am sure the appraisal knocked their socks off. The guy is literally clutching his heart as he is being told.
I am sure that man's family will find other pictures with the blanket somewhere in the photo. I am sure they can pin down the time frame the foster grandfather had in which to meet and get to know Kit Carson. And the ancestor must have done something to merit that blanet. Though Kit may have devalued Indian possessions, I am sure he was informed of its great value.
That blanket was extremely valuable from the day it was woven. It may even be possible to figure out who wove it, from the gov't records surrounding the "Long March" which was the finale of Kit Carson's great swath of destruction.through the Navajo land. The Navajoes were too defiant for the gov't and they sent Kit to burn their crops and round them (and their valued possessions) up. Then they made them walk, men, women and children, to Fort Sumner in NM for a lengthy exile from their own sacred lands.. This was a trauma that is still spoken of often on the Navajo Nation.
I lived in Window Rock, the Capitol of the Navajo Nation, as a teenager in the mid-fifties. I learned all about the Long Walk just by the way Navajoes were still reliving it as family memories.
I have one more thought. The unraveled Bayetta is finely woven wool from red uniforms- I forget whose, and the period it was in use, which is easily dated, was when the repair was made. It has the look and feel of a Navajo repair, so that should be worth something in the quest for provenance
Oh one more thing, the Chief's blanket my friend found in the yard sale was from later. A lot of bayetta wool went into the design, though it was still just stripes. I think it was the bayetta and a couple of generations of skill that encouraged the expansion of patterns in Chief's blankets. Then various dyes came in and more elaborate patterns.