IIRC, the question of his “exposed brain” is addressed in Irving Wallace’s book on P. T. Barnum, The Fabulous Showman.
The consensus seems to be that he did not, in fact, have his brain exposed. Rather, a portion of the casing which serves as a cushion between the brain and the skull was exposed, which is icky enough.
In addition to his accomplishments as an explorer, Adams appears to have been one of the great “travel liars” of all time, having claimed to have sighted camels and elephants, among other things, in the wilds of California.
In Jack Finney’s book Forgotten News there is a brief item about how Adams had a grizzly he killed made into a chair, and sent it to President Andrew Johnson. The head served as an arm rest. While pretty much anyone else would have thanked Adams and then stuck the chair away in an attic or given it to The Smithsonian, Johnson appears to have genuinely liked it, and kept it in the oval office.