FYI there may be ways for truth to prevail if the claim was a lie.
In a different but related context, I learned from Rav Reuven Weiner of Kollel Iyun Hadaf —
If a person, after admitting, claims he made a mistake and wants to retract his Hoda’ah see Choshen Mishpat 81:23. The Rema and the Shach differ about when the retraction is effective.