China doesn't own them all - it can just produce them the cheapest (like it does everything else). From the 2nd page of the article:

'"So there really is no shortage in rare elements, and in fact, there are enough deposits out there to easily fill demand, but at a price," he said.

At least until now, rare-earth production was not very economical, but if prices stay high, we will see many new mines outside of China, he said.'