Another interpretation might be that neither Bob (any version of me) nor Quincy created Doug, any more than a radio creates the music it plays. They somehow received information about him across the gulf between universes and interpreted it as the product of their own imaginations.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.