2 years in the caribbean, transfer to romania?

Is it true that if any part of your medical coursework is done in a non-approved school by CMB's list, then you're automatically out of luck for obtaining residency in California and other states that use California's list?

The Caribbean school that I went to is not the Big 4 and not on the list...if I transferred to an approved school, will CMB just recognize the school that I got my diploma from?

And yes, I know that Romanian English programs are not approved, only Hungary, Czetch, and Poland are...the question is hypothetical...

Thanks :)