If you're still in the US (as I assume you are), check the phone book to find the closest FBI office and call them to ask what you should do.

Most countries don't require you to be fingerprinted in order to get those police clearance documents. It's a peculiarity of the US system, due to the fact that there is no "national police" agency.

I can't believe this is the first and only time they have encountered this. (If your wife's condition has a name, it means someone else has had it.) And, oddly enough, the people at the local FBI offices can be remarkably helpful if you contact them directly to explain the situation.
Cheers,
Bev