Jam, as far as the casino question goes I can't comment because my community doesn't have one. In fact the people voted against a casino in two separate referendums. Our sister reserve on the Quebec/Ontario/U.S. border has one but I don't know how they distribute the profits.
As for alcohol it depends on the individual, like with any other ethnic group. I can drink most people under the table but my sister is toast after two drinks. I'd say it's a myth. Alcohol abuse, however, is endemic in certain communities because of the lack of economic development and rampant social problems.
What is sorely lacking is a focus on social programs and economic development. My reserve is relatively well-off because of the close proximity to a major urban centre and the tobacco trade, which provides thousands of jobs. The Canadian government, however, is fighting tooth and nail to crush this source of economic activity, however, deeming it illegal. In fact, the Harper government spent over 100 million dollars last year on surveillance, policing and harsh new mandatory minimum jail sentences for people involved in the tobacco trade.