It must be recalled that what "evidence" we have is based on written accounts which, it must be stated, are not unbiased.
My googling has unearthed the 'fact' that it was rumoured for a long time that Breakenridge, who never married, was homosexual. This appears to be based on one or more books written after his death.
These rumours may have been spread by, amongst others, Wyatt Earp's wife, Josephine.
...There was probably no occupation in the West that did not have lesbian and gay participants. William Breakenridge had worked as a Union Pacific brakeman and joined the Third Colorado Cavalry before becoming a deputy sheriff at Phoenix and then Tombstone, Arizona Territory in 1881, where he was known to, and accepted by many of the mining town's community. He was later appointed Deputy U.S. Marshall and finally a special detective for the Southern Pacific railroad. After Breakenridge's retirement, former Wells, Fargo & Co. detective Fred Dodge joked that "Billy was a nice young girl in those days, and undoubtedly today is a nice old lady." Josephine Earp, who with her husband Wyatt knew Breakenridge for many years, later declared that "the one thing I can say in his favor is that he avoided the liaisons with the dance-hall women who so enamored his associates."
Homosexuality in the American West
However, it should be noted that Earp and his wife were not fans of Breakenridge who was considered to be anti-Earp during the Tombstone days.
In 1928, he [Breakenridge] became a published author with the release of his memoirs of life in Tombstone and the old west, Helldorado: Bringing the Law to the Mesquite. Critics of the book, including Wyatt Earp and his wife Josie, claimed that much of what Breakenridge wrote was biased and more fiction than factual. Although Breakenridge met with Earp in Los Angeles to interview him, the picture he painted of Earp was less than flattering.
One can only conclude that, although not essential to the plot, the films writers/creators considered it accurate enough to have Priestly portray Breakenridge as he did.