Well, I said that history consists of accounts (stories).

I agree that what I (and most historians) call "historiography" could be called "meta-history". But that activity already has a name; we don't need to construct a new term (with a Greek prefix and a Latin suffix) to stand-in for a word that already works fine.

Historiography isn't some handwavey version of the past; it's the study of how historians do their work. That's the word historians use. Honestly, I think your history teacher got the wrong end of the stick.

Like, Humpty Dumpty had a point: you can use words to mean whatever you want. But it's not helpful for intelligent discourse to redefine commonly-understood terms.