That's a pretty inaccurate mischaracterization of how those operations work. Typically the FBI doesn't arrest someone until they have planted or attempted to detonate the fake bomb.

Of course, it's debatable whether they would have done anything at all without the fake terrorist

Not often. If you read the transcripts of the recordings made in such cases (which are often attached to the indictment as evidence, or sometimes available in audio form), the sad fact is that some people run towards the honeypot at full speed. It's entrapment to encourage a reluctant or uncommitted person, but there are quite a few people who are eager to engage in such behavior.