If my OP title is wrong then you can provide us with that Federal law.
What is someone charged with when they are brought before a judge?
Answer; Knowingly making a false statement – 18 U.S.C. § 924(a)(1)(A) – ATF commonly uses this charge for straw purchasers who knowingly made false statements to gun dealers or in the records that gun dealers are required to maintain (Form 4473).
My too lengthy OP goes on to further describe how the courts currently interpret this law to mean that for such falsity to amount to a fraudulent scheme or artifice...the falsification has to be a material misrepresentation. In order to be material, the falsification has to have resulted in an unlawful or prohibited person obtaining the weapons.
For a law to be violated it must exist.
On page 58 of The U.S. Department of Justice Office of the Inspector General Evaluation and Inspections Division Review of ATF’s Project Gunrunner November 2010 it states;
“ There is no federal statute specifically prohibiting firearms trafficking or straw purchases.” It goes on; Consequently, ATF agents and federal prosecutors use other criminal statutes to charge individuals involved in firearms trafficking crimes. These statutes carry relatively low sentences, particularly for straw purchasers of guns. The Sentencing Guidelines also provide short sentences for firearms trafficking-related crimes.
http://www.justice.gov/oig/reports/ATF/e1101.pdf