"We take the alleged actions of Mr. Banach very seriously, and we will not condone lying to federal agents," U.S. Attorney Christopher Christie said."
This is a way to attack the 5th amendment through the back door.
It's very close to making "failure to confess" a crime.
Apparently you don't understand the 5th. It doesn't mean you have the right to lie, it means you have the right to not answer.
You can keep your mouth shut, refuse to speak, remain silent.
Lying is not part of the privilege.