Best example: Martha Stewart. Stewart was not convicted of stock trading fraud; she was convicted of lying to a federal investigator -- which is a federal crime.
How do you avoid such a charge? Don't talk to a federal investigator of any kind, for any reason, ever, on or off the record. It's always on the record. Worden's Rule 1: Stick your tongue between your teeth and bite down until the blood flows. Do not admit to anything. Especially, do not deny anything. Remain mute, no matter how long they try to drag the interview out. Even if an attorney representing you is present, say nothing unless in the privacy of his/her office.
They will show you evidence that you did something. You will be tempted beyond most human ability to resist to explain that evidence away. Don't do it. Don't agree to any kind of test, be it polygraph, blood test or even taking your fingerprints unless they force it upon you, but through it all, remain silent.
They will tell you somebody said something incriminating about you, or that you were somewhere or that they said you were doing something or did something. Remain silent. Do not admit to or deny anything. If they ask you how you're feeling, say nothing. If they ask you if it's raining and you know it is coming down like Noah's Flood, say nothing.
Worden's Rule 2: Force the law enforcement agents to work only with the evidence they have. Do not allow your attorney or yourself to provide them with any defense you plan to use if you are charged with a crime unless and until you are in court and testifying to a jury -- if that is necessary or wise at all. That way, they have to guess what defense you plan to use, which makes it much more difficult for a prosecutor to prepare the case they have against you.
Never speak to anyone, especially a cellmate in jail, about your case and how innocent or guilty you are. Remain absolutely silent on the matter, and especially during telephone conversations. Law enforcement officers largely depend on suspects to try to talk their way out of a situation so they don't have to spend time in jail. When they do talk, everything they say gives the law enforcement agent places to go, places to look, people to talk to, etc., and that additional input often is what lands the suspect in prison, guilty or not. Law enforcement agents will tell you they are only trying to eliminate you as a suspect. You will be tempted to help them. Don't do it. Stay absolutely silent no matter how guilty they will say it makes you look.
Wordens Rule 3: If you are charged with a crime, the only time it counts for you to offer an explanation is in front of the judge or jury hearing your case -- and in most cases like that, it is still better you don't testify at all because when you do you can be cross-examined by the prosecution.
Worden's Rule 4: Never allow your attorney or yourself to waive your right to a speedy trial. Prosecutors and investigators use the time you are waiting for trial to develop more evidence against you. By demanding your constitutional right to a speedy trial, you shorten the time they have to build a stronger case against you. You reduce the time a witness might be identified or located to testify against you. If they proceed with prosecuting you with the shoddy evidence they have and you are acquitted, they cannot try you again for the same crime, even if you walk out of the courthouse after an acquittal and admit to the press you did it!
Look at what happened to Scott Peterson. Not only did he talk to the Modesto cops, he allowed interviews with reporters that were later used to paint him a liar. Had Peterson remained absolutely silent, no matter how guilty it might have made him look, a lot of the "liar" evidence used to convict him would never have been made available to the prosecution and the jury. Getting back to the feds: The federal government made it a crime to merely lie to a federal investigator.
For that reason and that reason alone, don't talk to a federal investigator, ever, about anything. They enacted and enforce that law, so it is best for every citizen not to speak to a federal investigator about anything, ever. They can't charge you with lying to them if you haven't spoken to them.