The one from the dictionary you cite been the definition for the 40 years I've been a scientist.
Webster seems to be defining
NATURAL SCIENCE as a subset of
SCIENCE, notice that the definition of
NATURAL SCIENCE takes you to a new definition. Strangely enough, that definition says absolutely nothing about requiring the data to be interpreted within any one philisophical framework. Therefore, why would any scientist want to restrict the framework in which objectively measureable evidence can be interpreted?