GRAMMAR

So I'm away from home and catching up on some reading. I just finished a book written in first person and noticed, for not the first time, 'I' instead of 'me' used in the narrative.  Such as...between you and I... and also ...with you and I...

Is this deliberate because it's from the heroine's point of view and she doesn't know that 'me' is the object of prepositions while 'I' is for subjects? Or am I wrong about the correct use of 'I' and 'me'?

This bothers me -- like I'm so great at English grammar myself!