SuperBeagle, I am American and spent the first 25 years of my life in America, and I am telling you that just because you have "never heard them pronounce it any other way" (in the one or two regions of America you might have visited, or on the television shows/movies you've seen) does not qualify you to speak with any degree of comfort about whether or not all/most Americans pronounce this word, or any other word, in the way you believe.
I am also fluent in Russian, and your belief in the correct pronunciation of Putin is incorrect.
Maybe stick with what you know.