In short, we might distinguish between several varieties of belief here:
1. Scientists collectively and historically decided a priori to adopt methodological naturalism, without ever having seen any evidence as to how it works. This view is possible, and it seems to be what Leiter and Myers thought they were refuting.
2. Individual scientists working today begin their analyses of any new problems by having defined "science" as excluding supernatural possibilities. Collectively and historically, they have adopted this method because it has worked before. In that sense, it is a posteriori. But as to any new problem, supernatural solutions are ruled out from the start. In that sense, it is a priori. While one can quibble over the definition of a priori, even a generous interpretation leads to the conclusion that this is how most scientists behave, and I can't see why any sensible person would disagree.
3. Individual scientists working today do not rule out any possibilities whatsoever. If there is evidence for the supernatural, so be it. There may not be any such evidence, but that is purely a contingent matter. Whatever the evidence shows is where we should go.… This view is not often claimed by scientists.
"More on Leiter" (09 Apr 04) (typography corrected; my boldface emphasis).
Leaving aside for the moment the serious logical problems and indefensible factual basis here—the two bolded assertions are the opposite of my experience as a science student and in conversation and engagement with scientists—notice that this discussion concerns only the "correctness" (or, more properly, "validity") of Inscrutable Design as a philosophy. Also leaving aside the distinction between proximate cause (explainable thus far only through evolutionary theory) and first cause (illuminated by, but not adequately explained, by current evolutionary theory, and perhaps illuminated by, and definitely not adequately explained, by Inscrutable Design), note that the argument never engages with pedagogy in public schools.
Math is often invoked as a "language" of sorts for the sciences. So, then, what does mathematical education tell us about how to teach science? Well, for starters, one doesn't get into imaginary numbers, non-Euclidean geometry, stochastic processes, and so on until very late in high school if at all. Instead, these advanced concepts, which are certainly "real" in the sense that they have immense impacts on the world we live in—for one thing, the solid-state electronics that you are using to read this depend on imaginary numbers—are reserved for later. In basic high-school math, one lives by the parallel postulate.
Similarly, the distinction between classical and quantum physics is not an issue until after one completes the first year of college-level physics. (Yes, it is referred to in college-level freshman chemistry, but one must pretty much take the physics on faith when studying basic analytic chemistry—irony intended—and in any event the descriptive nature of the material does not require students to use quantum physics.) Does the fact that quantum physics is not taught until later mean that concentrating on classical physics excludes the "religion" of uncertainty from the classroom? Of course not.
The real problem is that one is not prepared to consider first cause until one has an adequate grounding in proximate cause. Inscrutable Design attempts to conflate the two, but it cannot, for a very simple reason: Nothing in anything Inscrutable Design has ever asserted can explain the "evolutionary" trends one can observe in even recent history, such as the mutation of HIV and the annual struggle to figure out what goes in this year's influenza vaccine. At least at the highschool level, a science class is working with students struggling with the concepts of proximate cause and the evidence necessary to reason from it. Inscrutable Design would be a pedagogical nightmare, similar to trying to teach French and German in the same classroom to students with no prior familiarity with either. That is not to say that a high school can't teach French; it just can't hope to do so effectively in a German classroom without seriously harming the teaching of both. <SARCASM> I can just see a mandatory warning sticker in German textbooks to the effect that German designations of gender cannot be considered definitive because German includes a "neuter" gender not included in French. </SARCASM>
If one wants to teach Inscrutable Design in the context of US history, or a basic course in philosophy, so be it. Under no circumstances, however, does it belong in a high-school-level science textbook. Whether one considers the boundaries between the various disciplines to be valid or not—for example, much of modern biology would have been considered chemistry at the start of the twentieth century, and in turn much of modern chemistry would have been considered physics—those boundaries have proven useful in beating the basics into the heads of reluctant students. Without the vocabulary and knowledge base provided by "traditional" science education, students are not prepared to evaluate Inscrutable Design, or evolutionary theory, or anything else.
And that is precisely the problem: Inscrutable Design proponents don't want a comparative evaluation. The ID movement instead seeks to substitute faith for reasoning. Whether science offers a complete explanation of all that is in the universe is open to question; that current scientific knowledge does not is admitted by science. Requiring a method of reasoning that itself holds that its knowledge is incomplete to either offer a complete explanation of everything or be rejected in its entirety is the same kind of "black and white" argument that underlies miscegenation statutes. Understanding ID may be useful to some in understanding the complete context of the world; for example, one simply cannot understand what was really going on in the Scopes Trial without at least some understanding of creationist theory, and the obvious hypothetical from there can create useful classroom discussion in a history classroom. The real question is whether trying to teach these beginning ice-skaters how to do a triple Axel, when they have not yet mastered skating backward, is sound pedagogy. The answer is pretty obvious if one's objective is to actually educate individual minds; unfortunately, it is also pretty obvious if one's objective is to indoctrinate unthinking robots, and the latter is the actual objective of putting Inscrutable Design in the high-school science classroom.
Believe it or not, there is actually a publishing-law corollary from this material; it will need to wait for another time.