If they are already on the no-fly list, it would seem some due process has already occurred and this is not simply the work of one government servant. Don't forget the defense is free to say whatever they want but the government does not have the same luxury in, especially in national security cases, won't let out details even if they could. We're not getting the full story yet, nor should we at this time.
You cannot be serious. The legal definition of the term "due process" means precisely the opposite of what you are suggesting. Did you possibly mean "due diligence?"
There's no due process to get on the "do not fly list." You have to go through some kind of process to be taken off the list if you're on it by mistake.