Put yourself in the shoes of a federal agent investigating a crime. Crimes happen all the time; they're commmitted by people who then try very hard to hide what they did.

So a criminal investigator is going to treat everyone they interview with suspicion from the start. That suspicion is not a personal failing any more than a software QA tester who doesn't trust the latest build. It's inherent in that type of job.

And investigators only have certain tools that they can use in order to find the criminals who are lying to them. If they get information the wrong way, even if it is accurate information about a real crime, it will be ruled inadmissable and the criminal will get away.

A big tool they have is relationships. If they can get one person in a criminal network to cooperate, then they can try to traverse the network and find the other criminals. Since criminals rarely want to cooperate with law enforcement, they use "gotcha" type tools to compel cooperation--like the false statement trap. They just need a little leverage on the person to get going.