Somehow I feel like the people that are serious about this
  level of criminal activity, and capable of actually 
  accomplishing it, aren't first announcing their intentions 
  on twitter.

If you're in the secret service and you let the president get assassinated, it would be much more embarrassing if the assassin had announced their intentions in public.

Once the assassin has been identified, if they had a tweet from a month ago saying "I am going to assassinate the president in a month" you can bet that will be on the front page of every newspaper, making you look like an idiot.

And if your anti-embarrassment system should prevent a real assassination, so much the better.