They wouldn't. That's the point I've been trying to make several times over...
These Dog Soldiers are not called Churchill's fake Dog Soldiers.
Here is a chronology about the murder of an AIM member named Anna Mae Aquash.
The Lakota Dog Soldiers are mentioned and in a way that seems to be authentic. The killer of Anna Mae, Arlo Looking Cloud, may have been a dog soldier:
"Looking Cloud recieving, and having the gun would be consistent with Lakota traditional ethics dealing with Dog Soldier protocal. Graham was not a Lakota, and a woman would not generally have been assigned the responsibility of dealing with Lakota Dog Soldier business on Lakota land, therefore, it is more likely that Looking Cloud originally did have or recieved the gun."
http://www.jfamr.org/trialtime.html
I can't say how accurate this chronology is, but it does mention the Dog Soldiers and post it for that reason.
Here is another referrence to Dog Soldiers:
"DeMain has included more detailed versions of the alleged events, naming three individuals he believes were involved in Aquash's kidnapping. In DeMain's view the kidnappers (one of whom he claims was also the trigger man in the execution) were acting on orders from above. "These boys wanted to be dog soldiers," he says. "They wanted to be in the gang, they wanted to be important people. They were already doing security and toting around guns. So when someone in the movement ordered Anna Mae's pick-up, they went and did it."
http://www.citypages.com/databank/21/1002/article8432.asp?page=3
There's a certain amount of facetious sarcasm with the incredulity there. My Dad taught N. American Indian history at the U of I for 4 years while he was getting his masters and running the ROTC program there. To this day (after an illustrious 18 year military career which included that teaching stint) he'll stand behind the plains and northwest tribes warrior societies having produced some of the finest tactical fighters to have walked the planet.
My personal favorite of that era is Chief Joseph of the Nez Pierce. I've often thought someone should have had the balls to have let them "slip by" when they ran them to ground shy of the Canadian border. That was an epic trek and fight...