That contradicts with the article. The article states that the Muslim scholar theorized that god actively mutates the animals that want to adapt, i.e. god didn't just invent "the mechanism" of mutation, as you say.
This theory is a pastiche trying to use the "good parts" from Darwinism and is clearly worse than the original
Anybody claiming this, just don't have a deep understanding of mutations. Mutations are not a god's gift. Maths and science predict that they happen randomly, and most of the time they carry terrible consequences.
Lets take for example the people that inherited the butterfly skin syndrome. With a so fragile skin that it rips from the shoulder to the waistline at the minimum brush. Do this girl or this boy wanted to "adapt" to have a insufferable pain all the days of this life?
I seriously doubt that anybody would have asked for that. Lets be serious.