But if the forger claims his name is John Smith (or his date of birth is xx/xx/2004) he will edit the human-readable part.

If he pairs the edited human-readable part with a real barcode copied from a real license in someone else's name, then anyone inspecting the license will see the documentation matches his claim, and if they also use this site to check for fake barcodes it will confirm the barcode was really issued by the California DMV.