Sounds to me as though your teacher is being strictly correct about Continental Purl.
I’m an English knitter who’s gradually swapped over to Conti and for what it’s worth, this is what I’ve read up on.
True Contintal Purl is done how your teacher described but it seems to be mainly used in COMBINATION knitting, which is knit stitches done the regular Conti way but the Purl twists the stitches. It means knitting through the backs of loops on the next knit stitches to re-orient them and having to make some pattern changes as well.
I got Maggie Righetti’s, Knitting in Plain English, over Christmas and she said she refused to teach the true Continental Purl to her students because it was just too complicated for most beginners to get their heads around.
From what I’ve read on KH most knitters seem to be very happy doing the Conti purl stitch as on Amy’s videos - it seems to be the most popular way of knitting.
Hope this helps