I wouldn't be so categorical. Regarding assessing causality, with an appropriate choice of instruments (food prices, tax on specific food categories) one could use instrumental variable regression to disambiguate the relationship. I'm not sure if this is standard practice in this field but a quick search seems to indicate this has been done before.

As to why one would think nuts have protective effects at all -- I'm not a nutritionist, but from what I gather nuts do seem to have some desirable nutritional properties (high on unsaturated fats, protein and minerals), so that assertion doesn't seem that far-fetched to me.