Do you really expect them to go around claiming to have forged the document or putting their own name on it? And if they don't, nobody knows this, so nobody ha

Do you really expect them to go around claiming to have forged the document or putting their own name on it? 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?