I think you are reading it incorrectly. (It shouldn't be read as "Or so...")
Or so John said in, and out of [...]
"So John said" means "That's what John said".
Please click on the link (definition #5, the ninth example sentence): http://oald8.oxfordlearnersdictionar.../dictionary/so
I hope my response will be of some help to you.
Student or Learner