True, but your way lacks any scientific credibility, and therefore should not be taught in a science class. It's only an issue of classification. Teaching it in philosophy or religion class is fine with me.
If you allow ID in the science class, you're paving the way for astrology in an astronomy class, or crystal therapy in med school. If it weren't for the scientific process, we'd all still think polywater and N-rays were real. So if you want people to accept ID as science, allow it to go through the established process rather than redefining the process to match your needs.
I consider that to be a non-sequitur of sorts. Qualified, precise language, as well as mild disclaimers, are honest ways of presenting what we know and why we claim to know it. Such things belong in a science class precisely because it is fraught with philosophical and religious underpinnings. To extrapolate from the admittance of ID the admittance of every disjointed notion is to introduce a red herring. There is a measured and mature way for both atheistic and theistic assumptions to be brought to bear if/when necessary.
The debate is overblown in a way, because even though most school textbooks present only the atheistic point of view, they do so only slightly, yet without good reason; they state with confidence things that should be stated with qualification, but they do so within an exceedingly limted framework, little of which is germane to empirical science.
As for astrology in astronomy class, I think that would be a good way to introduce the subject since astronomy stands on the shoulders of those who first observed the stars and tried to make sense of them. That is to say, astrology contains a fair amount of science. And by now you know I grant a wide meaning to the word "science," similar to that of Alamo Girl.