The way I got the hat without killing a ranger was because I was going to Nipton and I went through Primm Pass (the ravine with the deathclaw and the dead Bright Brotherhood member) and I accidentally led the deathclaw all the way to Ranger Station Charlie where it began attacking the rangers, I ran up to the tower on the right side and then sniped the deathclaw with my service rifle. I went down and grabbed the ranger brown hat off of one of the dead rangers. I didn't mean to kill them or anything (I side with the NCR) but it was a happy accident.