Well, no -- that's you building a strawman.
What I'm contending is that your version of "science" says something equally ridiculous; namely, that as a matter of formal science it is impossible, ever, to recognize something as having been created, rather than arising as a result of natural processes. That is the logical result of saying that the ID hypothesis is "untestable by Science."
Further, if we take your position as being that of "Science" (why the capitalization, btw?) then "science" won't even try to test it, because it a priori assumes it's impossible.
Which is not a very scientific approach, I'm sure you'll agree.
And, as it happens, there are actually scientifically accepted tests for intelligent design in fields such as archaeology, to test the hypothesis that a particular object -- a rock, say -- was "manufactured" into a tool or not.
And, of course, you and I both have seen things in the woods or on the beach that are clearly created objects, and we recognize them as such despite the fact that they came from "an unknown agent acting for unknown reasons using unknown powers and abilities."
For you to somehow hypothesize that humans are somehow incapable of extending this power of recognition to biological manipulation is more akin to a religious belief. It's certainly not a scientific one. And, indeed, I believe I have sketched out for you above a kind of biological equivalent to the aforementioned archaeological test, that would apply to genetically engineered organisms.
So your allegedly scientific position would seem to be distictly lacking.