No one reported him taking the stone out and displaying it to prove the truthfulness of what he was saying.
And yet, now our historians claim it's "likely" that Joseph used this stone to produce the Book of Mormon.
Church Museum of History and Art.
Apparently Oliver didn't get the memo that he and Joseph were wrong about the Urim and Thummim because we now "know" that Joseph didn't actually use the Urim and Thummim. Instead, he just stared at this stone in the hat (SITH) and didn't use the plates.
Either that, or Oliver just forgot to mention the stone in his pocket because he knew Joseph didn't use it to translated the plates.
When Cowdery returned to Church membership in 1848 he spoke to an Iowa conference. His words there were recorded by Reuben Miller: “I wrote with my own pen the entire Book of Mormon (save a few pages) as it fell from the lips of the Prophet as he translated it by the gift and power of God by means of the Urim and Thummim, or as it is called by that book, holy interpreters. I beheld with my eyes and handled with my hands the gold plates from which it was translated. I also beheld the Interpreters. That book is true. … I wrote it myself as it fell from the lips of the Prophet.”