The key feature of the lawsuit is that the individual cannot show any specific harm was done, only that their legal rights were infringed. Most aspects of civil law require that the person show some sort of injury. In this case the specific law does not require damage. Damage to consumers is assumed as automatic if the company does not comply with the law. The wording of the law is only about compliance, not about harm.
And that is great and all, but also at point, how do you prove you were passed up on a job because of this without a company coming straight out and telling you the reason? There is no law that says a company needs to tell you why you were not chosen for a position. Your resume may simply be tossed into the "do not trust due to lies" pile automatically by the automated compute checking system that performed the check of the information in the resume with the information in the automated background checks, and you would simply be filtered out without even having an interview.
THAT is the point that this lawsuit is trying to bring to the forefront. This kind of data IS being used by many places for finding potential employees, new clients/consumers, loans, and many other use cases. Things that you write in your resume are being cross-checked against other sources and if things don't match, well, lets just say your word then becomes suspect, which is not a good position to be in when trying to get a job.