No, suspicions and assumptions to not make probability math irrelevant.
Until Southack provides a source/link or the math under discussion, I will not debate his particulars since we have no idea of the whole.
ID asks, "How can we calculate the odds of this poofing into existence in one step, under currently known conditions?" The ID question is not science. It is anti-science. It is hostile to inquiry. It is hostile to curiosity. It is fundamentally motivated by belief in original sin, the belief that the desire for earthly knowledge is sinful.
Science at its core is playful, inventive, imaginative and skeptical. Yes, science invents just-so stories. Yes, science publishes wild hypotheses. The difference between science and previous modes of knowing is that science puts its ideas and stories to the test. Testing is never over. Nothing is ever proved. Even great ideas like relativity and quantum theory are known to be incomplete.
But science does provide an enormous level of confidence in the reliability of its oldest ideas. And common descent via modification and natural selection are among the oldest, most studied, and most confirmed ideas in science.