A supernaturally directed natural process would be a supernatural explanation though wouldn’t it? The analogy of seeing intelligence breaks down at some point because your i-phone designer and plumber and Shakespeare and criminals investigated by forensic techs and humans investigated by archaeologists all operate under natural laws in the natural world and follow recognizable patterns that we have lots of experience with. When we are talking about THE intelligent designer of creation, we are talking (at least I am, be cause I believe the creator is the God of the Bible, not aliens or some generic force) about an intelligence that acts outside of natural laws (and therefore can’t be described by science).
I think the issue is, how do you study supernatural processes scientifically? That is kind of what the whole ID endeavor has failed to propose. I believe the world is intelligently designed. I think God guides evolution. I think this is intuitively evident through the eyes of faith, and it is specifically claimed to be true in God’s revelation that he is the source and Creator of everything and that creation has a purpose and he is working out everything according to his will and plan.
I don’t think the tools of science equip us to prove God is the creator, to scientifically describe how he guides evolution, or to tease out from nature which specific elements are “supernatural.” So I don’t see how you come up with an a “competing hypothesis” that is actually testable scientifically. Since I don’t believe that science is the only road to truth, this doesn’t rule out accepting supernatural realities, it just rules out proving them with science. This is where I don’t see your begging the question complaint. It’s not that the conclusion “there are no supernatural explanations” is asserted at the beginning. I accept that there are supernatural explanations. I just assume “there are no supernatural explanations proposed by science” as a premise.