Maybe the term “liberal mormon” had its origin at the University of Utah with a group of men who were referred to as the “swearing elders”.
This is an interesting and revealing history from Hugh Nibley’s life. This account makes it clear that Hugh Nibley was first and foremost a testimony bearing member of the church.
From Hugh Nibley’s: A Consecrated Life, p. 160.
At some point before his 1955 debate with Sterling McMurrin, Hugh was invited to speak to a meeting at the University of Utah, of the “Swearing Elders”-a group of liberal Mormons associated with Utah universities. After giving his presentation, Hugh says they took him aside and told him “You’re among friends now, you can say what you really feel about the Book of Mormon.” Hugh simply bore his testimony that the Book of Mormon is, in fact, a true record of ancient people and that Joseph Smith was a prophet. “Oh, were they mad,” Hugh states. “They were just boiling.” He recalls one member of the group launching into a harangue about the Book of Mormon and how “we have to get rid of it. It’s driving the best minds out of the church! You can’t see it, but with my training, I know it. Joseph Smith was a deceiver, but he was a sly deceiver.” Hugh was chilled by such reactions: “They had a real active hatred of the Book of Mormon.” These were, for the most part, members of the Church in good standing.
From the same book, page 159, Hugh in a letter to Sterling McMurrin makes an interesting comment about the church, along side another testimony:
…I am stuck with the gospel. I know perfectly well that it is true; there may be things about the Church that I find perfectly appalling—but that has nothing to do with it. I KNOW THE GOSPEL IS TRUE.