The web page that discusses the technology (link here) does have a mistake. In the video at the bottom of the page, the material engineer states that a "non-Newtonian fluid does not obey the laws of physics." [2,3]
It is precisely because a non-Newtonian fluid obeys the laws of physics that we observe unusual physical behavior like shear-thinning or shear-thickening. A fluid that did not obey the laws of physics would defy gravity, or it would spontaneously separate into its individual elemental components.
[1] I could not find an explanation for this abbreviation.
[2] Brooks is traveling the country with a vat of cornstarch and water advertising the new technology. For other videos of shear-thickening behavior, go here.
[3] I left a comment on the Brooks blog, but either it was not approved, or was removed.
[3] I left a comment on the Brooks blog, but either it was not approved, or was removed.