Earlier quoted context omitted.
It's not "cessation of ideas and thoughts", and the fact that the story gets it wrong could mean that science gets it wrong, which suggest science will never figure it out.
The language in the article is not clear. Perhaps this post in lifehacker better explains what happens to the brain during meditation. http://lifehacker.com/what-happens-to-the-brain-when-you-med... So why would I want to shut off my brain?
Have you considered the possibility that beta waves are not the best indicator of brain activity? A couple of pretty graphics with colors demonstrates only an interpretation of a certain signal -- whether or not a low signal means the brain is "shut off" is entirely up to interpretation.