You're right. This is market dynamics, not government.
However, when any market becomes profitable, it catches the eye of the government as a potential source of revenue. Mining is an already very regulated industry for very good reason.
The point I'm making is that should this sector become profitable (it has the potential to), will the government impose new regulations on it not yet imposed on the mining industry. Or, in other words, will there be new rare-earth regulation? This again would give China the upper hand.
It will be interesting to watch and see.