A patsy is "in on it", whether he is aware of his role or gets double-crossed. Oswald acted exactly like a patsy from start to finish. Google "Thomas Arthur Vallee" (see my avatar) for Plan A. Oswald was Plan B.
As far as being an asset is concerned, Oswald was a singleton agent sheep-dipped in the fake defector program headed by James J. Angleton who was the Associate Deputy Director of Operations for Counterintelligence at the time. He took over for Allen Dulles after he got canned by JFK for his role in the Bay of Pigs fiasco. Dulles did not go quietly into the night and is the architect of the Big Event. Otherwise, what the hell was he doing on the WC? He was best buds with Angleton who extorted Hoover into the mix with a compromising photo. It was an easy sell, however, because Hoover was the defacto boss of the mafia and already hated JFK. They all hated JFK. The Big Event was officially "on" once Johnson got onboard. Watch "The Men Who Killed Kennedy" for more background.
Hello Jack
A patsy is "in on it", whether he is aware of his role or gets double-crossed Fair remark, however, Oswald being an intelligence asset wood make it much easier to double-cross him or being the only way possible in order to establish garanties.
Oswald being an intelligence asset would demand a cover up Frome A HIGH LEVEL, permitting the murder being committed on a LOWER (LOCAL) LEVEL and generally demanding less people involved ...