Perhaps the best way to look at this question is to analyze some of the underlying assumptions. First, the "Homeric" works that have been transmitted to us, including Iliad, Odyssey and the Homeric Hymns, were not originally written works, nor did they have singular authors. Instead, they were elements of "oral epos", a body of traditions encapsulated in poetic form that were performed orally. The specific contents of each performance varied, but many popular stories were repeated in varying forms by the "rhapsodes" who specialized in reciting them. "Myth" is another name for elements of oral tradition that refer to gods and heroes. Thus it is not really accurate to think of Homer as using myths, but better to describe epic and myth as two aspects of ancient Greek oral tradition.