The federal form asks if this purchase is for the person filling out the form. Sarah had to lie, to purchase the gun without also putting her son through the background check.
For you or me that's a 5 or 10 year felony.
This is a straw man purchase, Sarah Brady is a illegal gun runner.
See page 3 of form 4473 at the top under IMPORTANT NOTICES. She seems to have clearly violated Delaware law, however.
Form 4473: http://www.atf.treas.gov/forms/pdfs/f4473pt1.pdf