A photon doesn't need to carry a UUID for people to conceptualize a difference between a photon going through free space and being absorbed and re emitted. The parent comment asks the right question, what is being meant by "the same" is required to know before being able to say the discussion makes no sense.
Taking your first literal interpretation as the only way the discussion could have value is no more helpful than this exchange:
"I'm going to the store, do you want the same hot dogs we have in the fridge?"
"That doesn't make sense, the store can't have the same hot dogs we have in the fridge".