Background check

Iowa -- I have spent the last two years training for a new career in the medical field. I recently applied at a Family Clinic in a nearby town. I received a job offer pending a favorable background check. I accepted the job and signed a form for the background check to be ran. After all, I have nothing to hide. Then I got a call from the hiring manager saying that my background check showed I had a founded report of child abuse listed on the states child abuse registry. She said they were emailing me a form to fill out. The form basically just asked me to describe the incident. There IS NO inicident. How can I fill out a form detailing an incident that never happened.
I have never had a founded child abuse report. The next day (after a very sleepless and upsetting night) I called my local Department of Human Resources office and inquired about the report. The lady took my name, ss # and birthdate and told me she would check. She called me back about 15 minutes later saying that my name wasn't on the registry. I called the HR department of the hiring company and she told me to fill out the paper stating that there was no incident and sign it. She also said the report came back with possible adult abuse and possible felony convictions. That is impossible. I have never even been charged with misdemeanor. Only minor traffic violations. The paper was to give permission to check further. My question is can they refuse to hire me because of false information, how do I prove it is false, and what are my legal rights? Even if they hire me, how do I go about clearing my name for future background checks?