The way I understand Axe’s argument is that evolution is false because the proteins do not fold right. This argument has a serious problem in that it says that Nature and by implication the Creator of Nature, Who is God, cannot do some thing when we know that God can do whatever God chooses to do. Also if one bases one’s argument on current science, current science is subject to change, which seems to be what happened here.
Axe & Co. are looking for the God of the gaps, Who makes evolution work even if it can’t. Of course human thought often does not anticipate the way nature works, because our thoughts are not the same as God’s thoughts. However God does have thoughts and nature follows God’s thoughts. We use science to follow God’s thoughts, not to know before God knows.
Non-believers do not think that God designed evolution, but they cannot explain the rationality of the way nature works. For Christians it should be simple, God is the God of the Facts, not the God of the gaps.