That's sophistry and confuses the issue. One is absolutely not acting as an FBI agent when forging FBI documents. There is a clear and common-sense difference between impersonation and forgery, and you seem to be misusing language to willfully misunderstand the difference.

When you're forging the document, you are not pretending to be an FBI agent. You are being a forger. The forger then claims that the FBI made the document.

Saying, "The FBI made these documents and here they are" is fundamentally different than saying, "I made these documents and am with the FBI." They do not collapse into the same thing.

To be honest, I still would hope forging FBI documents is a crime in the same way that impersonating an FBI agent is a crime; however that's a matter of law. It is a matter of fact that forgery and impersonation are different. One is falsifying documents, the other is falsifying identity. If you want to say that both can be reduced to falsification or deception, sure, but that's not a crime. Forgery (falsifying documents) and impersonation (falsifying identity) are crimes, and separate ones.

I think it's fair to say that someone creating a document with FBI letterhead/signatures/etc. is pretending to be an FBI agent.

And if they don't, nobody knows this, so nobody has cause to think that they are an agent. They can't really impersonate an FBI agent to themselves because they know that's not true.

Thus, if nobody thinks they're an FBI agent, how can they have impersonated one?