The answer is a bit complicated.
Without having completed a residency in the US or Canada, you are not Board Eligible. Many, if not most jobs as a surgeon in the US require that you be Board Eligible, if not Board Certified. To do so, you must complete a surgical residency in the US. Recently, the American Board of Surgery has announced that they will offer partial credit to those who have done some surgical training abroad...but you have to be already in a US residency program in good standing and your PD must apply for the credit. Up to 2 years credit can be claimed if approved by the ABS.
However, there are a few situations in which either a surgeon is recognized as an international expert in their field and is recruited by an institution or accepts a job which does not require BE/BC. These are generally pretty rare and are not to be considered as a route for *most* surgeons who have trained abroad.
Passing the USMLE Steps 1-3 only confers upon you the possibility of obtaining a medical license in the US. It does not replace doing a residency and most states require a certain amount of graduate medical training before you are eligible for a license (in addition to passing Steps 1-3).
So, the short answer is that if you can obtain a US medical license and find a job which does not require you to be BE (and remember, that many insurance companies are now requiring you to be BE as are many hospital credentialing boards), then you do not have to repeat a residency here in the US. But for all intent and purposes, most find that it is very difficult to do (ie, find a job) without the US training.
Finally, Puerto Rico is a US territory and as such, many of its schools are ACGME accredited, as are many of the Canadian programs. For graduates of these, they are treated as if they were trained in the mainland 48 states. You've mentioned Israel in a couple of posts; while Sackler and Ben Gurion students have obtained residencies in the US, they are still considered foreign medical grads and as such, subject to ECFMG certification and the same requirements for BE as if they had trained anywhere else outside of the US and Canada.
As always, the best advice is to train in the country where you want to work...if you want to be a surgeon in the US, do your residency here. If you wish to stay in the EU, then train there.
For further information, go to the American Board of Surgery site:
http://www.absurgery.org