SayUncle has the story.
Basically, a guy has a registered, relatively cheap, NFA firearm. Say it's a MAC-10, serial no. 1000. He cuts the serial no. section out, makes a receiver for a high cost NRA, say a BAR, and welds the serial number in. Then he sells it with the assurance it's perfectly legal. BATF will process the Form 4. Serial number and mfr match a registered gun, and so the transfer goes thru. I suspect the processing is by people who know little about firearms, and thus don't wonder why a MAC-10 is in .30-06 with a 24" barrel.
Eventually, of course, the matter comes to light and the gun is contraband.