Actually was able to read that one, if only with the help of my reading specs.
So, it appears that the young Claiborne, for whatever reason, admired (idolized?) the older Ringo and considered him a friend, perhaps even some sort of mentor. How Ringo perceived Claiborne, on the other hand, we do not know. Did he consider the kid a confidante of some kind? Did he share with the young man some of the more life-shattering, intimate details of his private life?
In any event, when Claiborne learned of Ringo's death it appears to have traumatized him to the extent that he took it upon himself to, as he saw it, "heroically avenge" what he considered his idol's murder, while dismissing or denying the possibility that he could have committed such an unthinkable act as suicide, that is, if he even was capable of conceiving that Ringo could have done such a (as he saw it, crazy? cowardly? taboo?) thing despite the fact that, if certain sources can be believed, Ringo made no secret of being susceptible to suicidal ideation.
So Claiborne, traumatized, grief-stricken, hyper-emotional, rage-filled, not thinking clearly but in dire need of a target or scapegoat to, in the context of his own value and belief system, explain Ringo's death in a way that he can process and accept i.e. makes sense to him, settles upon Leslie as the likeliest candidate to fit his pre-conceived scenario. And the rest, for young Billy, is history, which is to say the violent, bloody end of his.
Do we know how others in Tombstone and environs viewed Leslie's Claiborne-alleged involvement in Ringo's death? Did Claiborne's and/or Ringo's friends and familiars believe that Leslie was involved? How about the denizens of Tombstone? Was Leslie's alleged involvement, as I suspect, purely a figment of Claiborne's deranged imagination, or was there a widespread belief that Leslie was the killer, or even a fair amount of gossip? I suspect that there was no such belief because if there was, Leslie would at minimum have been questioned about it by the authorities, and we have no indication that that was the case, do we? All we know is that it was determined he killed the kid in self-defense.
Left unanswered, then, is why Leslie later, in Yuma, claimed to have been Ringo's killer, if in fact he wasn't. I haven't read the DeMattos/Parsons book--have you?--but perhaps an answer reposes in its pages, some manner of psychological insight that would in some measure explain what I will characterize as the violent, unstable, yarn-spinning--the man was famous for his fanciful stories about his florid past--Leslie's motivation behind making such a claim.
(I'd note that the newspaper article here reports that Ringo was shot in the heart, which prompts one to wonder what else they may have gotten wrong.)