You know I know at least one Section 31 supporter who thinks that Koval wasn't playing 31 like a fiddle.
I always assumed that he was.
In fact didn't this very thing pop up (non-canon though it may be) in at least one of the novels? IIRC, Koval was intentionally feeding Section 31 false data so they would investigate spies that don't exist, or go after the wrong people, etc. I don't know if he was actually working for the real Romulan government the whole time, or if he was playing both sides against each other, but it seems obvious that Koval is not a "real" Section 31 operative.