In my experience my heavy ash precision sounds a lot brighter my alder one. That could be due to the maple fingerboard against a rosewood one though, but I can't work out why that might make a difference if body wood doesn't. Body wood may not make the biggest tone difference of all the possible variables, however I believe it can make a difference.
If anyone believes otherwise, it makes no difference to me. They can believe in Pixies, Eskimos and a magic man that lives in the sky for all I care.