Actually, not. Read what you wrote carefully.
The material world can be the result of supernatural forces, or maybe extra-natural would be a better word; but that doesn't mean that it still cannot be tested or measured by the same scientific method used when the assumption is made that the world is the result of *natural* forces.
The scientific method is useful for collecting and organizing data collected. It's useful in that it gives scientists a universal guideline to follow so that another's work is reproducible and there's some sense to it.
It does not give scientists any reason to make philosophical assumptions about the world in which we live. Those assumptions are subjective and the result of philosophy. The assumption that everything has only a natural explanation is just that. Since science only deals with the *natural* and not what it labels the *supernatural*, then making philosophical determinations is way outside the scope of what science is capable of, therefore there's no basis for those determinations.
Philosophy is Philosophy, and despite Science once being called “natural Philosophy” it is distinct in that it can explain and predict natural phenomena based upon natural causes.
I had a great Molecular Genetics teacher once, a Russian anti-Lysenko exile who would ‘bless Ronald Reagan every day in my prayers’. He said ‘it seems to me that when you don't have any facts or a theory to explain them, all you can do is wax philosophical’.
You have no explanation for why a bacteria would intentionally increase its mutation rate in response to stress. The theory of evolution through natural selection of genetic variation has an answer at the ready. Science assesses theories based upon their explanatory and predictive powers. Evolution through natural selection of genetic variation has VAST explanatory and predictive powers.