The FBI and other federal investigative agencies have always picked the "low hanging fruit" when it was available. For instance, Martha Stewart was never guilty of insider trading but when she allowed herself to be interviewed about that subject by federal agents, she apparently told a fib or two. She was indicted for that and that is what she was sentenced for. It is a violation of 18 United States Code 1001 and scores of other statutes to tell lies to federal agents or fill out forms for the Government with false answers. Thousand of people have been sent to prison for violating the false statement laws. It seems clear that most of those people did so without realizing that it was a separate crime to speak falsely to an agent.
Now, the feds may not be able to pick that fruit so easily. In a recent filing the Solicitor General, who speaks for the Justice Department has taken the position that if a person is charged with making a false statement the Government must prove that the person knew it was a separate crime to lie to an agent. Most courts disagree with that position so hang on for litigation.