"I think Intel copyrighted the High-K design, so if that's true, then AMD is either still using SOI or another improved process."
Nope....
Intel uses bulk silicon, the same thing they are talking about in this article. High-k just refers to the transistor gate material. They also use low-k materials. High-k isnt a type of silicon, its just talking about one small piece of the chip.
AMD uses SOI, which is different from bulk silicon. They also use both high and low k materials on their chip. They aren't using hafnium yet, which is intels current transistor gate material on the 45nm note, but they do plan to use it at the 32nm node i believe.