I think what reasonable Creationists claim is that their Hypothesis, Theory, Speculation, whatever you want to call it, is indeed consistant with the evidence. If it wasn't consistant, it would not only be an issue of faith, but a laughably misplaced faith.
Then there is the SETI crowd that actually believes that there is intelligent life in outerspace. This is the same crowd that looks around and says everything we see is NOT the product of intelligent design, it can't possibly be - impossible! It must absolutely be a product of pure random chance! Then they gaze up into the screens of their employer's computer as it is busy processing SETI data knowing all along that their proof for life in the cosmos is finding order and intelligece rather than chaos.
What do you do with people who want it both ways?
One thing for which the naturalist cannot give account is the laws of logic: B cannot be both B and non-B; The ratio of a circumference to a diameter is 3.141592653etc.; A number, say "3", which exists in in its purest form as a transcendental idea which can neither be observed or nor touched. These things were not invented, but discovered. How does naturalism account for such truths? They are reduced to making them stand on their own, with not ultimate Cause. They just are.
We can look at the pictures in the clear night sky: The constellations have the same meaning among all people, yet their origins are shrouded in history. They tell a story, born in remotest antiquity and passed down from the very dawn of time. We see that all peoples have a Creation story, invariably involving water. Many have a flood story as well. These anthropological facts represent a gigantic hurdle to the naturalist.
The question is, under which system does the reality in which we live make the most sense? Solomon gives us a hint: "The fear of the Lord is the beginning of wisdom."