The Federal Agency has to be able to prove that they lied to the agent. This sound like a "he said/she said" deal to me and the only way that you could prove they lied is to get them to take a polygraph examination. Do you think they would voluntarily take such an examination?
Don't misunderstand me; I think they are lying too (but how does the Federal Government prove it?
Well, polygraphs aren't admissible in any US court of law. But, the crime of "lying to a federal officer" (covered in 18 USC § 1001 Statements or entries generally), frequently comes down to a he/said-she/said. It's the federal government that usually wins that argument.
Having said that, I would be shocked beyond belief if they actually pursued such an indictment, and even more shocked if it bore fruit in court.