Good point. Anyway, the original example reduces to this. After the first measurement [it doesn’t really matter which one is considered as first] we have a coup

Good point. Anyway, the original example reduces to this. After the first measurement [it doesn’t really matter which one is considered as first] we have a couple of complementary states +/- for the measured axis but it’s not well defined for other directions and in general a second measurement will break the symmetry.