The threat is real, though as far as is currently known has only been found attempted by one person: In 2010, Glenn Duffie Shriver, a study abroad student at Grand Valley State University in Michigan, was convicted of having taken bribes from China to encourage him to join the Foreign Service or CIA and to pass along U.S. secrets.
Shriver was spending the summer after his freshman year in Shanghai when he was approached by Chinese agents. He would go on to say he simply got greedy.
But the FBI believes there may be more Shrivers about to get coopted during their study abroad periods. So the agency has produced a film called Game Of Pawns: The Glenn Duffie Shriver Story, to warn students about spy recruiters.
The movie ends up being unintentionally hilarious, as many government-sponsored ostensibly cultural artifacts tend to be. It basically looks like an updated version of the shlocky anti-Soviet films the government used to pump out during the Cold War.
Plus, it's nearly a half hour long.
But in its statement on the production, the FBI says it wants American students traveling overseas to watch the movie before leaving the U.S. "so they're able to recognize when they're being targeted and/or recruited."
A better option would probably have been directing students directly to David Wise's excellent write-up of Shriver's case for The Washingtonian in 2012.
But if you want to see it yourself, here it is: