I think we can probably chalk this one up as more quackery designed to sell useless junk to gullible people.
Couldn't find a Bad Science article, but did turn this up:
A cursory search of PubMed did, indeed, turn up an impressive sounding study (“The biologic effects of grounding the human body during sleep as measured by cortisol levels and subjective reporting of sleep, pain, and stress”)...
... the above study was published in none other than the Journal of Alternative and Complementary Medicine, which means that it was either not submitted to, or was rejected by, journals that have any sort of legitimate reputation...
...these studies suffer from the same fatal flaws: No blinding at all, and no control groups at all. This means that the test subjects might as well have been wearing paper hats, and if told it would reduce their stress, it probably would have had the same effect. The small size of the study, 12 people, renders any result statistically useless; and my experience in such matters suggests there’s a good chance that these 12 people were very possibly employees and friends of the company selling the products.