Gaddis is stating a counterfactual here - suggesting that this is something that might have happened had nuclear weapons been used. He is quite explicit about this. In my copy, the next page opens with the clarification:

Only the press conference exchange and the events described in the first paragraph actually happened. The next two are fiction.

General MacArthur did push for the use of nuclear weapons in Korea. However, Truman was clear that there was to be no use of such weapons, as to do so risked escalating the war beyond Korea. As a result of this disagreement, MacArthur was sacked in April 1951.

offer a correction?

You are greatly misreading the passage, and I would suggest you continue reading beyond that sentence rather than immediately jumping online for a fact-check. The first three paragraphs the chapter are quite clearly a counterfactual scenario, where Gaddis is speculating what might have happened if nuclear weapons were introduced into the conflict. Notice how the next paragraph has the Soviets nuking Pusan and Inchon, and then MacArthur retaliating by nuking both the USSR and China, which is then followed by the withdrawal of many NATO countries from the alliance and hints that nukes were detonated over Germany too. This is how things went, in Gaddis' potential scenario, following the introduction of nuclear weapons into Korea.

Paragraph four then reads:

But is didn't.

Because none of that happened, and this is just an exercise in how "it might have gone".

Whether his scenario is the most plausible isn't suited to this subreddit, so I won't dissect it here, but try /r/HistoryWhatIf for that, perhaps.