It is true the Osage were considered "wild Indians" or sometimes called "half-wild" and the further west the "more wild" the tribes were. (This is not universally true of the Osage or any other tribe, for that matter.) The original roster of the 2nd Indian Home Guard of the Union Indian Brigade included Osage that were very disliked by the white officers and described variously as undisciplined, unreliable, uncontrollable, half-wild, wild and completely devoid of any concept of military practice. The Osage went AWOL on a buffalo hunt -- "they didn't do anything by another man's leave" (paraphrasing my favorite line from the movie Last of the Mohicans) -- and the officers were glad to see them go. When Drew's 1st Cherokee Mtd Rifles (CSA) defected and came to the Union encampment they were immediately enrolled in the 2nd IHG and the Osage were written off. With that said, I'd say the US military was completely incompetent in dealing with Indians, had unreasonable expectations, and made matters worse. The Confederates had some of the same problems but overall seemed to fair better. The Confederates had the advantage of a "character" like Albert Pike, many of the former US Indian Agents were Southern Men (like D.H. Cooper), and the Confederates had Indian officers which undoubtedly impressed and improved communication/understanding with the "less civilized" Indians.
It is also true, as you pointed out, that at the beginning of the war even the so-called "civilized tribes" appeared rather "wild" in some instances, e.g. Sparks' and others observations in late 1861. Those without guns brought bows and arrows but their use was apparently short-lived.