There is a 12 week rule in New York but you have the details wrong.
As an IMG, you are not allowed to do >12 weeks of clinical rotations physically located in New York state in hospitals not affiliated with your school. You can do as many weeks of non-affiliated rotations as you want anywhere else in the US, just no more than 12 can be in New York. You can't even really do this anyway, because IMGs must apply for approval from the New York State Medical Board for every single non-affiliated rotation they do in the state, and they would presumably reject your application once you reach >12 weeks. I also believe they ban you from licensure not residency, but I'm not sure about that.
The way the caribbean schools get around this is they have agreements with lots of hospitals to be officially affiliated in the eyes of the New York State Medical Board. Each school has a specific list of hospitals that their students can rotate through without being subject to the 12 week cap. As a Ross student I did 50 weeks of clinical rotations in New York state, 38 of which at "affiliated" hospitals and not subject to the cap, and 12 at "non-affiliated" hospitals subject to the cap.
And to answer the original question, yes you need letters from US physicians. It's not required but heavily recommended.