People with concussion symptoms really aren't supposed to do much of anything. No TV, no reading, no music, nothing. You're supposed to eliminate as much sensory input as possible. When you start reintroducing activity you're supposed to stop the instant you feel the least bit strange - headaches, dizziness, etc. You have to keep restarting a little at a time until your body stops reacting badly. It can take a really long time.
I'd imagine these guys have baseline testing done so it makes the measurement a little easier. You have to get back to your pre-injury benchmark without feeling symptoms.
For a person who is supposed to limit sensory input 5+ hours of airplane white noise +whatever else is going on, plus the motion of the plane (which makes some non concussed people nauseated), plus the car/bus ride to and from the airport, plus the rapid changes in atmospheric pressure, plus plus plus aren't really good for someone. Not to mention that if you get him there OK then he has some sort of major setback then you have to figure out the plane home. It's not like you can drive in an emergency.