I don't know when the last time you were in a classroom was, but they most certainly do teach in that manner!! It has been a little less than a decade for me, but I have been in classrooms on multiple occasions since that time. The approved textbooks in schools ensure that is exactly what is taught. "True American history" is a nonsensical notion of course, as ascertaining an essential truth is not going to happen, but high school history is about how great America is. We learned that the founding fathers are the greatest men to have ever lived. We learned about John Winthrop's comparison of American to a shining city on a hill. We learned about how the constitution is the greatest document ever created. We learned about slavery before, but of course we have white American heroes in that story, so it is ok. We learned about America saving the day in WWI. How we won WWII and stopped the evil nazis from their campaign of death and slaughter.
You know what we didn't learn? About the hypocrisy of our slave owning aristocracy who wrote things like "all men are created equal," and then owned some men as property. We didn't learn about the extermination of native Americans, except in passing. We didn't learn about the guilded age. The pinkertons crushing strikes. The homestead strike. The haymarket riot. The pullman car strike. Eugene Debbs. The colonialism of the Spanish American War. How the Soviet Union actually "won" the European war. Or at best American capital helped Soviet soldiers win the European war. We never learned that more than 80% of german troops at the height of the war in 1944-1945 were fighting the Soviets. We didn't learn that America did defeat the nazis, who were legitimately horrible and evil on a scale unmatched in human history, that we actually did terrible things during the war as well. Internment camps, fire bombing Tokyo, Dresden, etc. We didn't learn about American imperialism since the second world war. We didn't learn about the CIA overthrowing government around the globe.
So that is ridiculous. I graduated high school believing in cute and simple minded silliness about American exceptionalism. It took a college degree in history to lead me to question much of that nonsense. It took a masters degree in Middle Eastern Studies to make it all fall apart and for the true nature of America to be exposed. The reason you think America is exceptional is because YOU were trained to think that way in school, which kind of defeats your point entirely.