Overweight people (bmi 25-30) live longer. I bet they will eventually change bmi classifications to make that range normal. Underweight and obese people live less. But even there obese are probably better off than underweight. Being overweight is in itself exercise for the heart and your calves and every other muscle probably.
Is the study controller for income levels and status? Slightly overweight people might be benefiting from better healthcare and QoL. Afaik, there was only one Danish study which reached that conclusion.
Also muscular and fit people tend to fall within the overweight range of the BMI chart.
Tall people also tend to have a higher BMI as well (square cube law and all that), and Denmark is in the top 5 for tallest average population. I would have to imagine that would skew the results as well.
BMI seems like a useful tool for rough estimates of weight, but for any rigourous correlations it seems almost impossible to disentangle from other variables.