I don't agree with Mayor on every detail presented in her books, and I think she has in some places over-interpreted the evidence. For example, John Boardman, while agreeing in broad outline, made a compelling case in The Archaeology of Nostalgia (2002) that Mayor over-interpreted a skull on a vase as a fossil giraffe, mistaking a rock tossed at the skull for an anatomical feature. However, in general she made a clear and compelling case that fossils provided the skeleton (forgive the pun) on which the monsters of myth grew from generic conceptions to their specific details preserved in art and the later stages of Greco-Roman mythology. I'm not sure I agree that fossils were a prerequisite for myth; myth has always been with us. I think the fossils helped give shape to generalized, preexisting stories by providing physical proof of their reality for believers.
Well, do I have a treat for you. I've added to my site's Library both of these famous pieces. I found a rare 1806 translation of Cuvier from The Philosophical Magazine, and I have myself translated Abel from the German. Then, to round things out, I've also posted a fun little chapter from William D. Matthew about the close relationship between zoology and mythology in the pre-modern world.
[Click here for a correction of mistakes in this post.]