The CLEO signature is not a "permit" though some CLEOs use it that way. It only states that there is no law prohibiting you from buying the item. In a few cases, applicants have hired an attorney to explain that to the CLEO and sometimes have been successful. The threat of a messy lawsuit sometimes is also effective, though it might create a lot of rancor. The whole thing is really a cover for BATFE's collective a** in case a city or county council passed a law last night that BATFE doesn't know about.
But it has been used in family quarrels dating back decades, in political bias, in racial discrimination, and to solicit bribes from applicants. It should be abolished, but don't hold your breath unless a lawsuit gets to the right court.
New topic: Unless you are a Class 3 dealer/manufacturer, you have to have BATFE approval, in advance, to take any NFA item across a state line for any reason or any length of time.
Jim