You are missing the point. Yes, if you get a patent in the U.S. it doesn’t protect you in other countries (minus some specific circumstances).
But no, if I file a patent in the U.S. and you then run to another country and file a patent before my patent issues, your patent is likely not going to be valid. Because under the Patent Cooperation Treaty, if my application in the U.S. is likely to be prior art to your patent application, and therefore the other country will find your patent to be invalid.
This does not mean i have a patent in your country. It means you don’t.
So no “stealing” the patent.