Its a myth.
The parent will not reject it if you touch it.
Put it back and leave it alone(if you can).Do try to feed it.It doesn’t like humans.
Parent can see you looking up there and screwing with it and will stay away.
You scared the youngen with the saw.
Next year dont allow a nest to be built.This year remove that one some reuse them all season.
I have been watching one above my garage spot light...Came home yesterday and it was on the ground and all 5 eggs were gone.
Damn Blue Jay or Crow
DONT try to feed it