Oh come on... Its a propaganda video for the site/program. Of corse it makes sense :D, doesnt mean it true.
You have a thing called math in school, that sole purpose for most people is to get your brain going. You get enough problem-solving from this. Its up to you what you do with this.
Its the same with coding, knowing how to code wont make you smarter. But in time you will use the same concepts you use to solve code problem in real life, like splitting tasks to smaller ones and so on.
And also there is a diference between knowing how to code and understanding programing concepts.
Most schools(as far as I know) wil get you some basic coding knowledge, but that doesnt mean ****, you can learn this on your own pretty fast. Where schools(CS) kick in is delivering a broad specter of knowledge and serving it to you on a few-year program. Knowing why you did something, what goes on in the background and using math concepts with more complex problems, to make them simpler is what will help you in the long run. If you are into programing.
If not, then well... you dont need to code :P
If you wanna stay sharp, do math (not meth), solve puzzles, sodoku, learn a song and so on, it does count what you do with your time, just dont blame the schools.