Despite this, you still do not understand what a conspiracy is.
Very simply put, it involves more than one person.
The case you've cited is irrelevant, as the 'cop' isn't a conspirator, therefore a false dichotomy.
In the SFIO case, the conspiracy was between SFIO's CEO and promoter. If the FBI had not been involved directly, it would still be a conspiracy as multiple parties were involved.
Here's the verb. Perhaps that will give you a clue.
con·spire (kn-spr) v. con·spired, con·spir·ing, con·spires v.intr. 1. To plan together secretly to commit an illegal or wrongful act or accomplish a legal purpose through illegal action. 2. To join or act together; combine: "Semisweet chocolate, cocoa powder, espresso, Cognac, and vanilla all conspire to intensify [the cake's] flavor" (Sally Schneider).
You need an overt act in furtherance of the conspiracy to commit conspiracy only. It does mean the complete crime was ever perpetrated.