The Ninth Circuit has determined that making a false claim to US citizenship for the purpose of procuring private employment renders a non-citizen inadmissible. However, the court also found that the only way to make a false claim to US citizenship for the purpose of procuring private employment is through the use of an I-9 form.
The full text of Diaz-Jimenez v. Sessions can be found here:
http://cdn.ca9.uscourts.gov/datastore/opinions/2018/08/30/15-73603.pdf