I don't know about Native Americans being prone to alcoholism, but we did have one interesting experience a few years ago. We took a nice long driving vacation to Las Vegas, and we left a day early so as to do some sightseeing along the way. We stopped at 3 or 4 Indian casinos in New Mexico and Arizona. Most of them were quite nice, and just smaller versions of the normal casino environment. One, however, was quite different...we went in, and it was filled with Indians hooping and hollering, and having a good time. However, the place had a Stench of Booze and Vomit...needless to say, we didn't stay there long.
I imagine Indians are not much different from any other Ethnic group...some enjoy alcohol in moderation, while others let it rule their lives.