I don't know I wouldn't say Wyatt came off as a "real person" here but that is partially because of the dream like nature of the episode (which I absolutely love, it's one of my favorites from season 3)
True enough, he wasn't presented as a "real" person, but what is interesting is that the whole sequence was patterned after Kirk's knowledge and view of history. What Kirk knew (or could recollect) was used as "the pattern of their deaths" as the Melkot put it. And here we see Wyatt Earp and his brothers (as well as Doc Holliday) in an unfavourable light. It could be seen as Kirk's view of history running counter to what is popularly believed today and even more so when TOS was in production.
That said when you read up on the event and the people involved as well as what lead up to the event no one really comes across well. A lot of the Old West seems to be made up of bad men, badder men and a lot of those of dubious character.
I haven't read it in 37 years, but there is a book called TRIGGERNOMETRY that really debunks and demythologizes the actual gunfighters. The one detail I remembes is William Bonney on a staircase shooting down at the back of a guy at the foot of the stairs, less than 9 ft away, not even under fire, and missing him completely, only wounding him due to lucky richochet.
This thread was kind of neat timing, since I was watching ONCE UPON A TIME IN THE WEST this morning and just got BITE THE BULLET on blu ray too.