Perhaps a call to FDLE might get you a reason for the additional checks with the FBI. If not, you might consider calling Mr. Buckley or another attorney familiar with the process.
IF you were purchasing a weapon, in theory the same issue should come up and the FDLE would issue a temp. approval after a three day default period for clarification. I believe (but am not positive) you could then ask what the information was and who (what jurisdiction) submitted it. They may even be verifying that you are not the person with a similar name with serious background problems. I don't know how important it is to you or your situation but, if it were me, I'd get some legal advice on this and explore it as far as possible as to WHY.