From my observations of the testimony, the two men - Coats and Rogers - were in an impossible situation - they couldn't answer fully, as their testimony likely fell under reasonable Executive Privilege provisions, the Senators would not accept the answers they felt they could give, and they were carefully phrasing their answers to avoid lying, as that could lead to loss of their job, if not potential jail time.
From Wikipedia, about the Star Chamber of Henry VIII, which bypassed rules of regular courts:
One of the weapons of the Star Chamber was the ex officio oath where, because of their positions, individuals were forced to swear to answer truthfully all questions that might be asked. Faced by hostile questioning, this then gave them the "cruel trilemma" of having to incriminate themselves, face charges of perjury if they gave unsatisfactory answers to their accusers, or be held in contempt of court if they gave no answer.It's such situations that the 5th Amendment was designed for, to give protection to people accused by courts. Other means of stopping the power of the Star Chamber included Habeas corpus, which is used to keep people from being detained without a charge being brought (a common occurrence in the Star Chamber).