At a minimum he shoulda used “Juan Budd”.
Run John Budd through E-verify and see if how far it gets. My guess is that everything about the real John Budd is completely different than the illegal John Budd. Also, there is a good chance the real John Budd is dead. The employer does not want to know the truth. This farmer needs a deep on-site audit by the IRS covering the last few years. How do you think that would go?