"Perhaps if all high school freshman (or whatever) were required to take a course on "What is Science?" this debate would be over."
Have you seen many science texts, as used in High Schools? Virtually every one of them begins with a chapter on what the Scientific Method is. Biology, Chemistry, Physics...they all start with that first chapter.
An entire course is not needed. The chapter will do.
Then it is obviously not sinking in. If it did, would this debate even exist?