The classic example of the problem of induction is the statement "all swans are white". Yet this statement was demonstrated to be false upon the discovery of the Australian Black Swan. The logic is pretty simple behind this, if P is not true then ~P. So the statement follows that the discovery of the black swan is that not all swans are white. Not that all swans are black or even that all swans must be green. Yet this is the fallacy of the creationist.
You presume too much
The strategy is quite simple and much employed. Instead of building a positive case for special creation, it's proof by negation, if not natural cause X, then supernatural cause. So much time is dedicated to destroying "Darwinism" as if natural selection is the only natural cause that it could possibly be, and because natural selection doesn't work (in their eyes) it follows that it must be that God did it.
This line of argument suffers from bad logic. That if one thing cannot be explained by evolutionary theory in its current form, then all it does is highlight a hole in evolutionary theory. It doesn't follow that none of evolutionary theory could be true, or that it was created by God. Instead of recognising the new gap for what it is, it's taken that the entire theory is wrong and that special creation by the Judeo-Christian construct of God is true. In other words they have found a black swan and from there concluded that all swans must be green.
Bring yourself back to a time before 1858, and imagine yourself as an evolutionary biologist testing the then popular idea for evolutionary theory of Lamarkian inheritance. You want to demonstrate the mechanism in action so you take a lab mouse and cut off its tail. Then you breed the lab mouse with another lab mouse who also had its tail cut off. And to your dismay, the offspring have tails as do their offspring.
By the current creationist rhetoric of today, by that experiment you have proved creation! After all, the natural mechanism didn't work so there must be a supernatural mechanism at work. Of course the problem in logic should be obvious now. ~P just means ~P. It doesn't mean R.
The presumption made is that God is the alternative, so all they have to do is get rid of the current natural explanation and thus God. Yet in reality all it does is point out a gap in our knowledge. If Lamarkian inheritance doesn't work, then all we can take from that is that we know that Lamarkian inheritance doesn't work. So the presumption that if not current mechanism X then God is as absurd as concluding from finding a black swan that all swans must be green.
Because of the aforementioned presumption, any argument turns into an argument from personal incredulity. In the case of evolution, those who believe that destroying natural selection will mean JesusTM, no matter what they cannot be convinced of even the possibility of the process working. In effect, their whole case relies on not understanding how the process could work.
Consider some of the arguments that are used against evolution. "Evolution violates the second law of thermodynamics", "most/all mutations are harmful", "function X is irreducibly complex", "you can't get specified information by chance". Now such arguments have been demonstrated wrong or irrelevant many times before, I don't need to go over them again. But consider why such arguments are used.
These arguments rest on the premise that all swans must be green. If it did turn out that current evolutionary theory couldn't build irreducibly complex functions, what does that say about what did? It doesn't imply that God came down and muddled with DNA to create those IC structures.
To borrow the terminology of Dan Dennett, the creationists want a skyhook. They can see that there are cranes rising up high from the ground, so by destroying the crane structure they hope to prove that the skyhook will still be there. So whatever crane is being touted as the crane by which the hook hangs, attacking that structure becomes the goal.
By this stage in the game, there is already a concession that evolutionary cranes do exist. The microevolution cranes have proved impossible to knock down, so it is posited that although those cranes are real, they are merely hanging off the skyhook that is God. 150 years since The Origin Of Species and every attempt so far to knock down the crane of natural selection has shown the resilience of the crane, while discoveries of other cranes have been made. As yet, no skyhooks.
Since the whole enterprise rests on the false premise that all swans must be green, I don't expect this line of attack on evolution abate. The fact that there are any white swans at all means that there's going to be the persistent effort to firstly demonstrate that the swans only appear white, and secondly to search for any non-white swan to invalidate the premise.
If one bases their arguments about swans on observations, they are subject to revision upon future studies of swans. But if one doesn't even try to base their arguments about swans on observations, then they'll forever be trying to discredit evidence that doesn't fit their arguments. Whether one can reason philosophically that all swans must be green is irrelevant to the reality of the colour of a swan.