GAO came out with a report a couple weeks ago that some students were entering the country illegally and hadn't gone through the TSA background check. From AvWeb:
"The U.S. Government Accountability Office (GAO) Wednesday announced that at least a few foreign students entered the country illegally, were not vetted by the TSA, and were approved for flight training by the Alien Flight Student Program (AFSP). In its report, the GAO concluded that "weaknesses exist" in the specific strategies intended to diminish the potential terrorist threat from general aviation aircraft. The GAO noted that the AFSP "is not designed" to determine how a flight student entered the country and that more than 25,000 foreign nationals applied for FAA airman certificates (completed training) from 2006 to September 2011. Of those, GAO says a known number may not have been vetted by the TSA, and at least six flight students approved for training by AFSP have been arrested by immigration authorities."