This "currently accepted" explanation that has appeared in "multiple places" is news to me. Got references on it...?
I've never heard of the Republic as a test-bed anywhere... and you wouldn't WANT her to be a test bed if it was training cadets 20 years before TOS. It's far more likely that the Republic (NCC-1371) was one of the last of the previous-generation of ships still in service and NOT one of the first brand-spanking new Constitution classes for cadets to joyride in.