Returning to the latest Worst Idea Ever, even if you implement a "Do Not Ride" list for Amtrak, it would be impossible to do so in any reasonable fashion for the numerous commuter rail systems (many of which share track with Amtrak), rendering a mostly pointless security system completely pointless.
More than that, it's really unclear how preventing (not that it would) potential terrorists from boarding trains...achieves anything. The reason we want to keep potential "bad guys" from boarding planes is that it's not that most difficult thing in the world for a passenger to take a plane down from within. But a train passenger can do... what? Doing damage to trains and train-related infrastructure is much easier to do from outside the train.
