This is just a little side note expanding on a discussion between Ed Dove and myself in the comments on my post about fairy tale culture. I think we pretty much agree, but there may be some confusion because we may be talking about different categories of "fairy tales".
"Fairy tale" is another name for a traditional folk tale with fantastic elements. This is the base definition, and seems to be the one Ed is using. As I recall, Tolkien (in his essay "On Fairy Stories") was even stricter, requiring a fairy tale to include an actual fairy; thus, "Little Red Riding Hood" is not a fairy tale, in Tolkien's view.
However, there is also a literary genre called "fairy tales", said to be created by Charles Perrault and elaborated by Hans Christian Andersen, Andrew Lang, Oscar Wilde, and George MacDonald, among many others. It more or less began as an adaptation of traditional fairy tales, but with many cultural elements translated into what authors feel a contemporary child would understand. Thus, although there are kings, queens, and knights, there's not much discussion of the legal details of fealty, or the method a knight uses to support himself (working serfs in the field,) or details about war and combat maneuvers, church politics, technical discussions of medieval crafts, and so on.
And, more importantly for what I'm getting at, not everything in the fairy tale genre is a traditional European folk tale; it include fables, Greek and Norse mythology, King Arthur, Robin Hood, the Arabian Nights, and tales from many other cultures, retold so that it is not necessary to know the details of the source culture to understand the story. Plus, it includes a lot of original material as well, short stories in the fairy tale style. Wilde and MacDonald in particular were known for this.
At the time of D&D's creation, most adults had grown up reading Lang or MacDonald, or fairy tale collections very much like them. Even if they didn't go on to read Bullfinch's Mythology -- which was actually a requirement in my sophomore high school English class -- they would have been exposed to Greek and Norse mythology in fairy tale format. They would have known what a Minotaur, Pegasus or Medusa was (because those stories frequently get the fairy tale treatment,) and they would have known what a roc or djinn is (because Sindbad and Ali Baba from the Arabian Nights get the fairy tale treatment.)
So, strictly speaking, you can't get many of the original D&D monsters if you stick solely to traditional fairy tales, but you can get practically all of them with a wide background in literary fairy tales popular in the '50s, '60s and '70s. The exceptions are movie monsters and weird monsters (made-up, or borrowed from weird fiction or sword & sorcery.) And the weird monsters, I would argue, aren't intended to be part of the culture of the PCs; they're something from outside the PC's experience.