Thanks for passing this along; it's wonderful.
The answer that rings most true for me is Ralph Ellison's, and Bradbury seems to me to echo it somewhat: A writer writes and then reads what s/he has written and if s/he recognizes something symbolic, uses it or doesn't. (And may not recognize something as symbolic, though readers just might. Remember, the author doesn't know everything.)
I think for many, if not most, writers the idea for a story comes first and the ideas about what the story can expand into comes after the initial writing, the act of writing stoking the imagination. A lot of writers have said something along the lines of, 'I'm not a writer, I'm a re-writer'; the story doesn't usually come all at once, it accretes from tinkering with it, from adding here and subtracting there, moving this piece to that place, sanding off the spurs on the transition, plugging the hole where it came from, shoring up the part left behind. In the process the writer aware of symbolism and in favor of that symbolism will write to strengthen and support it.
Randy M.