you are not qualified to know whether you are innocent of wrongdoing under federal criminal law
Title 18, United States Code, Section 1001 makes it a crime to: 1) knowingly and willfully; 2) make any materially false, fictitious or fraudulent statement or representation; 3) in any matter within the jurisdiction of the executive, legislative or judicial branch of the United States. Your lie does not even have to be made directly to an employee of the national government as long as it is “within the jurisdiction” of the ever expanding federal bureaucracy. Though the falsehood must be “material” this requirement is met if the statement has the “natural tendency to influence or [is] capable of influencing, the decision of the decisionmaking body to which it is addressed.” United States v. Gaudin , 515 U.S. 506, 510 (1995). (In other words, it is not necessary to show that your particular lie ever really influenced anyone.) Although you must know that your statement is false at the time you make it in order to be guilty of this crime, you do not have to know that lying to the government is a crime or even that the matter you are lying about is “within the jurisdiction” of a government agency. United States v. Yermian , 468 U.S. 63, 69 (1984).
the only avenue for reform with respect to Section 1001 is in Congress
you can politely decline to be interviewed by the FBI agent. Tell the agent that you have an attorney and that “my attorney will be in contact with you.” If the agent persists, say that you will not discuss anything without first consulting counsel. Ask for the agent’s card, to give to your attorney. If you have not yet hired a lawyer, tell the agent that “I want to consult a lawyer first”
The absolutely essential thing to keep in mind is to say nothing of substance about the matter under investigation. It is preferable to do this by politely declining to be interviewed in the absence of counsel. … It is crucial to note that affirmatively declining to discuss the investigation in the absence of counsel is not the same thing as remaining completely silent.
You are not obliged to explain your decision to anyone.
I am not suggesting that you should obstruct the FBI or invariably decline to answer an agent’s questions. … Neither am I suggesting that it is generally acceptable to be interviewed by federal agents as long as your attorney is present. In fact, it is usually unacceptable and is often quite risky.
Source: How to Avoid Going to Jail under 18 U.S.C. Section 1001 for Lying to Government Agents – FindLaw by Solomon L. Wisenberg