So, to be clear: you are advocating some interpretation of quantum mechanics (for instance, but not limited to, the many worlds interpretation) where the measurement process is really measuring the system that produced the entangled pair?
I believe this interpretation fails to explain experiments where people have entangled particles with timelike separation [1], and then have shown that measurement of the second particle (which has never co-existed with the first particle in any reference frame) collapses the wavefunction of the first particle.
I'm not saying that the Copenhagen interpretation is the absolute truth, in particular many-worlds and superdeterminism are valid alternative interpretations, but I think the one you're advocating doesn't work.
[1] http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.110... (non-paywall: http://arxiv.org/abs/1209.4191 )