Multi-Criteria Decision Analysis (MCDA), which Nutt used, is a tool for decision making, not something "sophisticated" to generate scientific evidence!
I have not read the papper, but informing public policy ("decision making") seems to be what this study is trying to do.
I'm not sure what you mean by "informing public policy", but if the paper was to inform, they would provide summary of facts and facts only. The paper says it is trying to estimate drug harms using some set of arbitrary "harm parameters". I am saying you can't objectively estimate harms with an MCDA analysis. You're not going to get anything objective out of this unless you're framing it against an exact set of decisions you have to make. All you're going to do is find one group's interpretation. Although MCDA is systematic, and a lot of it including the ranking is generated automagically once you have everything set, overlaid with some "sophisticated" (Nutt's words in the interview) overtones, it is entirely subjective.
If you wanted, I could give you an MCDA showing cocaine is more harmful to society just by tweaking a few criteria a tiny bit. I could add a practicality criteria in that drinking alcohol is a cultural practice in many places, or I can separate two forms of drinking, responsible drinking and irresponsible drinking. There are so many ways to slice it that if you don't have specific decisions you're evaluating against, the whole analysis is useless.
I have not read the papper, but informing public policy ("decision making") seems to be what this study is trying to do.