Your question implies you believe that a placebo-controlled trial is the only kind of medical study that carries any weight.

This is not true. It's only one kind of study.

In this case, the study was looking for a correlation between diet and cancer diagnoses. All it needs to be valid is to conform to the scientific method. Placebo-controlled therapeutic trials are not the only kinds of studies that conform to the scientific method, and indeed not all of them do.

Please try to avoid reflexively invoking this trope to unfairly dismiss potentially interesting studies.