Comment by fluoridation

The only way I could see it counting as impersonation is if the LLM is able to call tools and has access to, for example, an FBI-relevant database, but there is no login or anything in front. So a random anonymous user can hop onto a chat and pretend to be an FBI agent and the LLM must somehow decide whether the person is really one before returning some external information. In that case, yes, lying to the LLM about being in the FBI would be impersonation, just as if you stole an agent's credentials and used them to log into the FBI's network. The LLM in that case is performing an authentication function that, say, ChatGPT doesn't.