Makes perfect sense to me. However- and I am not an English Professor either- I believe that ICOT was correct in omitting the comma and quotation marks. Here’s why:
Generally, when a sentence is introduced by the words “X said that” it means that the words to follow are not direct quotes but rather paraphrases. So I could say “ICOT said that she didn’t understand Joseph’s explanation” even though her actual words were “Your explanation was way over my head.”
Along the same lines, a comma is not required because it is not a direct quote. If I were quoting directly- omitting the “that”- my sentence would then look like this:
ICOT said, “Your explanation was way over my head.”
as opposed to
ICOT said that she didn’t understand Joseph’s explanation.
Does this make sense?