Fine-tuning, perceived to be so natural as to be a "natural occurrence" doesn't disprove God any more than the world, perceived to be so natural, disproves God. Martin Rees and Brandon Carr endorse the fine-tuning argument with this: “The basic features of galaxies, stars, planets, and the everyday world are essentially determined by a few microphysical constants and by the effects of gravitation….several aspects of our Universe—some of which seem to be prerequisites for the evolution of any form of life—depend rather delicately on apparent ‘coincidences’ among the physical constants.” Even Stephen Hawking concedes that “reduction of the rate of expansion by one part in 1012 at the time when the temperature of the Universe was 1010 K would have resulted in the Universe starting to recollapse when its radius was only 1/3000 of the present value and the temperature was still 10,000 degrees.” How is it logically convincing or relevant to claim that this happened naturally? If I deal out four cards to myself, and they are four aces, you'd be suspicious. But if I claim this happens all by itself, that wouldn't make you any less suspicious. Now suppose I do it again, and then again. I can claim it is happening naturally, and possibly it is, but the idea that "this game is rigged" would be in the front of your mind and make more sense to you.

The basic argument is that a fine-tuned universe, admitted by astrophysicists, plays very well with the idea that the universe has been created by a person God. It's a little more awkward in the "this is all a remarkable accident" card dealing scene.

It doesn't matter if physical realities can be explained by physical explanations. In theism, that's the point. In atheism, it's the result. So what? That doesn't make fine-tuning "provably wrong". A materialist would claim we have this fine-tuning because, well, that's the remarkable way it turned out, and if the universe were not fine-tuned, we wouldn't be here. That may be true, but how is it a logical and scientific objection to the idea that maybe there was a higher power governing the tuning? It doesn't.

We observe that the universe is remarkably fine-tuned, quite nicely for life as we know it. We have two hypotheses: (1) it was designed by a powerful and intelligent being, or (2) it has come about by a process of change that doesn't involve an intelligent designer. Given the logical parameters of the situation, the first choice has more logical credence than the second.

An important element of many cosmological arguments for God's existence is the fine-tuning argument: "The parameters of the early universe take on a narrow set of values that could allow for our existence." I don't consider this to be a strong argument in the first place, since any arguments from improbability must establish a prior probability for an alternate explanation, but the recent announcement that inflation of the early universe has been experimentally verified is also a strong indication that fine-tuning is not an argument for a designer. Here's why:

Physicists observed that matter was much more uniformly distributed across space than the hot big bang models predicted, giving space a seemingly arbitrary smoothness, and allowing for the existence of galaxies across the universe. A theist might have said "God fine-tuned the density of the universe to allow for galaxies", but scientists asked "what if it can be explained naturally?"

In fact, the only motivating factor for the inflation theory was the idea that apparent fine-tuning may be a natural phenomenon. The verification of the theory is a huge demonstration that assuming fine-tuning implies a designer is an intellectual dead-end, and in some cases, provably wrong.