Apparently at least one FBI counterterrorism agent did this very thing, on national television. I think you are seriously underestimating FBI agents' big mouths.

http://www.huffingtonpost.com/2013/05/07/tim-clemente-fbi_n_...

http://www.fbi.gov/news/testimony/going-dark-lawful-electron...

http://www.huffingtonpost.com/2013/03/28/fbi-surveillance_n_...

Edit: Note that this was well before the PRISM leaks.