What's wrong with the Sheriff simply calling people listed as references and telling them " I've got someone listing you as a background reference. Is there anyone you know who should NOT have access to a firearm?"

Think of the benefits. Not only would applicants not have to worry about their name or identity being disclosed, but the police would have plenty of new leads voluntarily offered to them regarding people they might not otherwise have been considering as individuals with character flaws.

IMHO - Using a tool like a telephone should probably require a license too - so we can make sure Mr. Sheriff is properly operating it.