None of this Ever Really Happened

Pete Ferry is driving home from work one evening when he sees a car swerving dangerously on the road. The driver is a beautiful, half-naked woman, and it's clear that something isn't right. He follows at a safe distance for a while, wondering what he should do - but he hesitates, unsure, and watches in horror as her car lurches forward, straight into a tree, killing her instantly...
This is the tale Pete tells of his class of high-school students. But did it happen or is it actually an elaborate concoction to illustrate the power of his story-telling to his restless teenage charges? Was it really an accident? Could Pete have prevented it? Who was the woman and why can't he stop thinking about her?