You were quoting a different poster from me that I quoted at the beginning of my post. I went on to make much the same point you are making. We are on the same page on this one. Although in my state "intoxication" is defined as being under the influence of "alcohol" or "controlled substances" to the extent one's driving is impaired. So, being impaired because of OTC meds, lack of sleep, caffeine, etc. cannot be a basis for an OWI charge.
You had better check that again.
"Impaired" is whatever the cop wants it to be.