People can swap wristbands,
Not very easily. They're designed to prevent this. That's the whole point in having them rather than a laminated badge or something.
"Hey, I'm going over to Syria to kill westerners and enslave Christians for the raping and whatnot..."
I guess the difference is between that and "Hey, I'm going to Syria for undisclosed reasons", when the possible legal reasons don't require a huge stretch of credibility. A complete stranger could be an aid worker, or a journalist, even a businessman (there is some trade even with US sanctions).
I think in this case, it's more a large number of borderline actions like this, and the DoJ are picking the ones with the best chance of success. Whether they should do things like this is something personally I'm undecided over.
Work without a vision is slavery, Vision without work is a pipe dream, But vision with work is the hope of the world.