I think we need a lawyer here, but this seems totally wrong. You're only committing a crime if you lie under oath, either to a court or congress. Cops lie to people all the time.

You should use your right to be silent rather than answer any questions of course, but that right disappears at the border.

Still, lying to a customs agent isn't a felony (at least not in the US). (If so, please cite the law). If you're not a citizen of the country you are entering, the most they can do is refuse entry. If you are a citizen, well there is where it can get complicated.