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.
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.
No doubt! But sometimes a revolution in interpreting the results of experiments is necessary for advancement. While current brain activity measurements may show low values for the measured activity under certain states, that does not, by any means, suggest that the brain is not operating.
http://lifehacker.com/what-happens-to-the-brain-when-you-med...
So why would I want to shut off my brain?