This is generally correct. One of the main effects of CRS being separate to FATCA is that a person from a CRS country like anywhere in the EU, UK, Aus, Canada,

This is generally correct. One of the main effects of CRS being separate to FATCA is that a person from a CRS country like anywhere in the EU, UK, Aus, Canada, NZ... many countries... can hold assets in the US itself which is not a CRS signatory.