Like any significant treasure or lost mine story (LDM, Adams, Victorio Peak, etc.) this one has its faithful believers and folks that are similarly convinced that it's a hoax. I can't get that link to work on my computer, so I can only speak of what I know broadly about the mine(s)...the fact that there are multiple locations only makes the story more difficult to make sense of.
The stories have more or less stated, Thomas Rhoades was given the opportunity to gather gold from an Indian site by Chief Walker (spelled many variations) of the Utes, on who's territory the mine was located. Some have speculated the "Carre Shinob" was a mine, others a cache site from earlier Spanish activities, and some would suggest it was both (and perhaps more). Thomas Rhoades dealings in mining and the Natives, eventually led him to a number of maps from a massacred Mexican mining group. While Thomas was only permitted to access gold from the Carre Shinob for the Mormons, the maps provided new avenues for gold that he could gather for himself. This new proliferation of locations is why you frequently heard of the Lost Rhoades MineS. As in more than one.
For many the biggest evidence in favor of the Carre Shib Ob specifically, would relate to the state of Mormon affairs. When they arrived in the Salt Lake Valley, the combined cash on hand for all the pioneers was reported to be less than $100. Within a year they were minting their own coins. Mormon gold was also considered to be "light", as in impure...with concentrations of silver and copper (I believe) in similar amounts to Spanish gold from the area that had been smelted into bars at the mines before being transported south. Thomas' time to collect and return with the gold suggested he didn't have time to mine it, which has led many to speculate he was recovering smelted gold from a cache site. There's nothing in the records to suggest the Mormon Mint was refining the gold either, so the idea that he was bringing in raw gold seems an unlikely one.
Thomas Rhoades would pass on his information to his son Caleb, who continued to access the Carre Shin Ob on behalf of the church, while also seeking and discovering his own claims through his father's maps and his own prospecting endeavors. Eventually Caleb was denied access to the Carre Shin Ob but continued to work some of his own claims. This would be complicated later when the Ute Reservation boundary was established and left Caleb unable to access the mine(s) he had been working. Prior to his death a great effort was made by Caleb to negotiate with the Ute tribe to access his mine, but his efforts were thwarted by rivals with more significant political clout who falsely believed they could find and exploit Caleb's mines. They never found them and Caleb died before he could finalize negotiations.
The newspapers form the 1890s to 1920s are replete with references to searches for these mines. Much has been written in the past 50 years as well. The body of literature is quite exhaustive, but varies in quality from "Reasonable and Interesting" to "What's this guy smoking?"
Keep in mind the Mormon Church as a body, has made none of these claims, and to the best of my knowledge takes no official position on the stories or the mines as a part of their pioneer heritage.
Hope we can keep this civil guys...this is a place to discuss treasure, not bash people's faith.