The story was invented scores of years later, probably. Because the Canaanites cities were obviously destroyed (i.e., there was wreckage), I suspect the tribesmen felt it was more exciting that they were the 'victors' rather than the 'survivors'.
As well, there's a theory that Egypt conquered the land of ... Midian (?) ... and some of the refugees came to Canaan and brought some of their religion with them. And so, the religion of the refugees mixed with the stories of the Canaanites, and the myth of Exodus and Moses sprung up.
And, to be honest, it bothers me that so many people don't know that the story of Moses is a myth. It's a widespread misunderstanding in our culture, and the churches don't have the scholarly base to correct it.