I'm not sure what you're trying to ask here, so if I'm not answering what you want please clarify.
Improper treatment would include taking part in activities that are specifically recommended against in recovering from a concussion. You can just look up the risks of inadequate recovery time from a concussion. It doesn't mean you're always going to have an issue, but when you are concussed you are at risk of further damage. Some people get rattled and they come back and they're fine. Some people get rattled, then they come back and they get rattled again and it's not good.
Second-impact syndrome - Wikipedia
If you would like take note that PCS can last for far longer than most people expect here:
Post-concussion syndrome - Wikipedia
It varies wildly between person to person how long they need to recover from a concussion and second-impact syndrome is serious business.
There is literally no problem with taking an extra week to make absolutely sure someone is not experiencing any symptoms, even mild ones, to avoid the risk of another head trauma. Getting a second concussion before you've fully recovered from a previous one is quite clearly more dangerous than getting another one once your brain has healed, and it can take significantly longer to fully recover from a concussion than people seem to think. Obviously ideally you won't have another one at all, but again I'm not really sure what you're asking for here because this is quite well documented so I assume I'm not answering the right question.
In all likelihood it's no big deal to put Pettersson on a plane if he wasn't experiencing any significant symptoms. It's also unlikely he gets another concussion if he comes back a game or two early. May not matter if he doesn't stay relaxed in a dark or dimly lit room. However,
sometimes it does and then it's a problem that was entirely avoidable. It's not worth the risk for these meaningless games.