This statement is only partly true: many did not sign anything at all ("did not admit their guilt"), but nonetheless they were sentenced.
More than that: we know about cases, when prisoners were given a term without ever having been interrogated on the charges! We received such information from people yet alive, who had been sentenced to imprisonment in exactly this way. We do not know, whether people were also sentenced to being shot without interrogation& there is nobody left who we could ask.