It appears that there is some validity to this technology. Not surprisingly, the published journal literature available is basically non-existent, except for a handful of patent applications describing something along those lines.
The title of one journal publication "Preparation of a filtering material using nanomaterials for removal of a heavy metals from wastewater" uses a diamond nanopowder to aid in filtering out heavy metals from waste water. The citation is "Antonenko, L. P., Energotekhnologii i Resursosberezhenie, 6, 2011, 49-54"
Additionally, there is a patent appplication from France (where at least one article I read cited as the technology originating from), title "Apparatus for activation and mineralization of water for domestic use". In this, they use a variety of powdered gemstones (diamond, ruby, sapphire) as well as precious metals (gold, silver) to filter the water.
Certainly, nano-particle scale materials are effective filtration agents, as most contaminants will not pass through such a small sized filtration device. The use of some gemstones (certainly diamond) are beneficial for their relative chemical inertness, and certainly silver is well-known for it's antimicrobial activity, and synthesis of gold-nanoparticles or gold-silver coatings are also actively under research