According to that company's 'About Us' page, "PrintScan’s certified fingerprint technicians undergo extensive background checks before being cleared with the FBI, NYS Department of Criminal Justice Services, Florida Department of Law Enforcement, and Homeland Security."
I looked up on the FBI website to see if they provide similar background check service, and sure they do for $18! I have a hard time figuring out why FL board of medicine uses a third party service instead of FBI to do background checks, and also wondered why shouldn't FBI background check be enough/sufficient for criminal activity (i.e. don't states share their criminal records with FBI?). All of this is to say that the existence of companies like PrintScan--and the fact that one of the state governments uses it--is definitely concerning to me.