I researched this a bit earlier this week but didn't save the links. Its not just that China could produce rare earth minerals at lower costs but western countries starting tightening their laws on mining (due to uranium byproducts) but also environments laws. Then they willingly shared the production techniques to China to do all the dirty work.
However US restarted its rare earth mining a few years back and now it ranks second in production through far behind China. I'm guess the main concern was the need of these rare earth minerals for military equipment.
I ask because this is one of the most common myths in Economics.