So, oddly enough, quantum mechanics is entirely local in the common meaning of the word. When physicists say that it is non-local, they mean that particles which have a common origin but then were separated can be stronger correlated than particles without quantum properties could ever be. I know this sounds somewhat lame, but that’s what quantum non-locality really means.This is correct. A particle has quantum properties if it obeys the Heisenberg uncertainty principle. A particle without quantum properties obeys a classical theory of local hidden variables.
The theory is local. The only claim to non-locality is just a statement about correlations.