This is correct. Betting, as a policy, helps distinguish between Orin(correct) and Orin(wrong), but is really only useful for eliminating Orin(spy) because it's a novel method that the King expects spies to yet be unprepared for, and is easily investigated if circumvented.

Imagine, If Orin is wrong and yet mysteriously has all his debts re-paid and shop re-purchased shortly after being punished, some eyebrows would be raised.