I agree to a degree. But the sad fact is, the West wouldn't be able to exploit the feelings of western China's Muslims if there weren't grievances there to begin with. You can't create something out of nothing. All the great powers do this, play on interests and desires to get favorable outcomes. China does it abroad, so does Russia. America does it pretty much everywhere.
But that also means there have to be some root of discontent pre-existing, as well. At least in my view. If China treated Uighurs fair or equitable, or gave them the same opportunities Han Chinese have, there wouldn't be discontent for Americans to fan the flames of. Same goes for when Soviet intelligence made inroads with black groups in the US during the Cold War, there was a simmering discontent already present.