Actually it is making such an argument: "Occam’s Razor argues for a simple theory: the net marginal impact of drinking on health is negative at all levels"
They don't provide definitive proof, but that is their argument.
That seems an abuse of Occam's Razor. There are many chemicals that are known to be unhealthy in large amounts, but are healthy (even necessary) in smaller amounts. This group of chemicals includes linoleic acid, vitamin A, iron, and water.
It may certainly be true that alcohol is a net negative in any amount, but it would be in lots of good company if it turns out that small amounts of alcohol are indeed healthy.
Sorry, I was unclear. You're right that they do claim that the impact of drinking is negative, but I don't think they made any actual argument in favor of that viewpoint.
They don't provide definitive proof, but that is their argument.