IMO, the point about the child getting the yellow belt isn't about the relative importance of the training in the life of the child versus the adult (from what I see it's normally the other way around, with the kids seeing it as more of a game) - it's about the child's immaturity and lack of life experience making them less able to deal with normal failures and challenges and delayed gratification.
You see it sometimes in the kids' class -- if there's a game where it's possible to win or lose, the 5 year olds often cry and are devastated if they lose. But the same kids by 6 they'd still rather win but they've learned to handle it with a more positive attitude if they lose, to understand that there will always be more games in the future and that they have a lot of power over how bad they let themselves feel. Usually by then they can shrug it off and talk to their friends...
Likewise you can see kids learn to understand that it's OK to not always get what you want IMMEDIATELY. You can wait a little, and you will get it eventually and enjoy it then, and you will be OK.
Absolutely! The problem here lies with parents that want to protect their kids from any type of disappointment and a society now that wants everyone to "win." No matter how badly you play you make the team or no matter how well your team does everyone gets a trophy. In the US, IMO, we are failing to teach the youth, who, let's face it, will become adults that have a childs mind, leading to ever more serious problems.