The FBI used to use hand written reports to record interviews after the fact and trick you to sign them...they would purposefully put in language that could mean you lied to the FBI agents...you then were forced to cooperate or face jail time.
The FBI can lie to you no end; if you slip up in any answer to them you are guilty and punishable. No intent to lie needed.
I can see almost no reason to ever talk to an Agent without a lawyer present and recording the session which usually means they cancel the interview.
I mean, it is not like the FBI has a record of integrity and honesty. Remember the vaunted FBI Crime Lab?