The statemtent "It is acceptable to use personal pronouns in a narrative essay," is true.
A narrative essay tells a story. It talks about a particular event or a series of events and describes the kind of experience that the writer (or protagonist) got from it. In a narrative essay, the story told is usually about a personal experience (so you will have to use personal pronouns). You also make a point with a narrative essay, so that, the goal is not only to tell an entertaining tale but also show the reason for the story and the importance of the experience.