When someone says the word for the punctuation mark, the decision about whether to put the word into the transcript or just the punctuation mark itself is really an editorial decision on the part of the reporter.
A person says: “It is the, cap, First, cap, Amendment discussion that is important.”
A person is reading from a document and says: “On the 15th of the month,” comma, “the surgery was performed.” [This sentence could be punctuated with a pair of dashes to set off the word “comma.”]
Whether to put in the word that was said or just the punctuation it stands for is an editorial decision on the part of the reporter. Maybe the question is “How verbatim do you think you need to be?”
There is justification in English for doing it either way.