Eva, what I meant by I found it telling is that by not denying Herndon's account of Lincoln's views on religion, it tends to give credibility to Herndon's account.
Generally a trustee deals with financial/legal issues, providing advice and acting as counsel in these ares. "The trustees, under their own chairman, have charge of the property and fiscal and legal obligations of the congregation." https://www.britannica.com/topic/presbyterian