I've got a theory how the Gs could have known that X was the BG, but it's a bit whacky.
What happens if the Gs want to recruit someone who is BG or D? According to this thread, this ain't possible
http://forum.juventuz.org/threads/27992-The-Mafia-Game-for-Dummies .
So let's assume they want to recruit X, and get told they can't -> they know X is a special. They know Radekas is the detective due to crooked cop as Radekas explained -> X is the BG -> they wanna lynch Radekas -> they put X in jail so he's unable to protect Radekas.
Now of course this theory also relies on a lot of coincidence, and they would have been lucky to first try to recruit the BG, and then actually recruit the Jailer. Or, as Alen claims he manipulated the jailer, meaning recruiting him wasn't necessary.
Which brings me back to how @Alen knew who the jailer was, and how he convinced him to jail X.
Seems mighty suspicious in hindsight, and adds to the argument behind lynching Alen. I'm thinking he should indeed be the guy to go for now.