I believe that I read, somewhere on this Forum, that a dribble can only occur inbounds, that an out of bounds inbounder is not actually dribbling the ball but, rather, is bouncing the ball, and since this player is not dribbling, this player can't double (illegal) dribble.
I'm having trouble finding relevant rule citations, other than the casebook play stated above, for this situation. How about a little help?