Usually, if I am writing that a person said something, I would precede the quoted text with a comma, like this:

Then he said, "I don't know why it happened."

However, in this sentence, an editor told me the comma after "he" wasn't necessary:

The author writes, and I'm quoting his words exactly, that he, “couldn't understand why it happened."

Which would make it read like so:

The author writes, and I'm quoting his words exactly, that he “couldn't understand why it happened."

I tried to look up the rules that cover this, but I'm still not clear if it's a matter of one version being more correct or not, or just a style preference. I fear it might be the kind of thing that pedants and would-be editors will complain about no matter which way I go.

Is either more definitively correct? If both are acceptable, is there a compelling reason I should choose one over the other?