Why is Peter no longer telling the story?

In Chapter 24, Peter turns the perspective over to Shakespeare to provide a less personal account of the events, but knowing Shakespeare, they might possible be embellished.

Until now I have told this story plainly, as it happened to me, but now the time has come for me to drop out of the picture for a while and tell you what happened as it was later described to us by Shakespeare and our other friends in London.