Sorry I'm late to the party on this one, I just saw this post. I'm also afraid that my answer isn't going to provide much clarification, but here it goes anyway...

Short answer to your question: we don't know that they did all that much (which isn't to say that they didn't...we just don't have evidence of it, and it doesn't make much sense that they would have).

Awesome answer, right? Okay, let me explain. Most outlaws didn't live long enough to write memoirs, and what little talking that we know of during their lifetimes didn't provide much in the way of a detailed explanation on where they hid, and with whom (for obvious reasons). Like a modern criminal or celebrity "outlaw" type, Billy the Kid, J.W. Hardin, or Jesse James didn't make a habit of telling strangers, reporters, judges, or other people who might have written down what they said where they liked to hide, who they mixed with, or what kind of interactions they liked to maintain.

So what does that leave us with? If we don't have a first-hand account from the source, or a verified primary source accounting from a stranger or public official, we have to look at testimony from those who claimed to have ridden with these outlaws. We can verify that some of these people did indeed (or didn't) ride with the outlaw in question, but depending on the source, one has to take what they said with a grain of salt.

So what little we know about outlaw interactions with people outside of established towns comes from accounts from those chasing the outlaws, or those riding with them. Billy the Kid has gotten about as much ink as any outlaw, and as a result, we know a fair bit about his traveling habits and the company he kept. The Kid spoke good Spanish, and was apparently quite the ladies man. It's well known that he had many friends within the Mexican communities of New Mexico and Arizona as a result, and when on the run, or moving cattle, he had many friends within this community to help him out. His interactions with Native American tribes isn't well documented, and would have probably been infrequent. Especially in Arizona, tribes like the Apache would have been actively hostile to most anyone not Apache. Less aggressive tribes would not have been eager to involve themselves in any dispute that put them at odds with the U.S. government or law enforcement, and thus probably would not have been much more welcoming to outlaw types.

We know that Jesse James didn't really have much cause or opportunity to mix with Native American tribes. James operated further east, and his brother Frank lived to an old age and to my knowledge never related any stories about the two making use of Native American allies. John W. Hardin was a flat out maniac and bastard, and didn't really have any friends, Natives included, so that's also out. You could say the same thing about Tom Horn.

So short answer: no, I don't believe that the historiography shows that Old West outlaws had much interaction with Native American tribes. It's a fair question, and perhaps there were times when an outlaw made use of a particular tribe with a friendly face, yet I've not read much about it.

[Sources - Richard Slotkin, 'Gunfighter Nation'; Michael Denning, 'Mechanic Accents']