It seems to me that the device is designed to detect lulls in brain activity in such a manner:

a. As we think critically on a complex subject our brain works harder, so the system detects this.

b. While we are day dreaming ('brain-fart', 'writer block', 'brain freeze', 'mind short', etc.) our brain relaxes for a moment, and the system detects this as well.

c. The study uses sleep as the control, at which it is assumed we are using our brains the least.

This may not be accurate because:

a. The test cannot accurately determine critical thought

Assuming the study uses a constant 'test' as a control, the participants will approach said test differently. The measured activity can not depict how challenging the material is because its difficulty is relative.

b. The test cannot accurately determine an 'error'

Suppose participants' lulls are composed of different thoughts. Perhaps one subject drifts into near unconsciousness, while another is mesmerized by the surroundings. One subject will have a noticeable drop in activity, while another seems to remain constant.

c. The low point of activity may be incorrectly measured

As you all know, certain phases of sleep will utilize the mind's power. It is assumed that the study determines the lowest point of brain activity during the participants' sleep cycle as a constant of zero. This may be the only valuable thing the study could have determined.

It seems that the PNAS is the best place to learn the specifics of the study.