Native Americans who do not drink or are recovering from alcoholism have no right to force their inabilities to control themselves on those who can control themselves. I have two recovering alcoholics as parents, and neither of them flee the gas station in terror when they pass the beer freezer.
Yes, because your anecdotal evidence clearly proves that Native American reservations shouldn't have the right to ban alcohol sales in their reservation. They are trying to combat alcoholism in their jurisdiction the best way that's honestly possible with the reservation government.
Local governments, nor state or federal governments, should have the power to regulate health matters that aren't literally a public threat, such as a contagion. It is up to the individual to overpower his addiction, not the state. This is unfair to those on the reservation who can control their drinking.