You’re strawmanning it.
To delay more than that which is attributable to transmission speed does require recording somewhere.
I did not say that recording causes delay.
You said, “To create delay greater than the transmission distance divided by light speed requires recording somewhere.”
I said that is not true. That is because it’s not true. You can record a signal without slowing it down. Well, before I get into any potential quantum physics fallacies, let me be more precise in my language:
You can not slow it down enough to be perceptible by human beings.
I did not say that recording causes delay.
You do realize that these two statements are incmpatible with each other, right?