actually it is a simple matter of linguistics and definition: super(above or beyond) + natural = that which is beyond the natural.
the natural sciences cannot study that which may exist beyond the natural.
When you lump intelligence and design characteristics with the supernatural you are defining terms to fit your preconceived bias. The only way to study intelligence and design is as natural phenomenon.
If you are defining naturalism as only that which is phenomenological you are reject such concepts as mathematics, principles of the physical universe, such concepts as random, and a host of other principles fundamental to the work of sience. You can not pour a liquid into a beaker without relying on nonphenominological reality. Reason, for example, is nonphenomenological but it is a basic component of any science.
You are correct, this is a semantic issue. Unfortunately you have defined yourself out of business.