Halsey's retelling of the events during that cutscene are said to not be entirely accurate, as the Elites present in that cutscene are all wearing Storm-class harnesses, which hadn't been introduced until after the Human-Covenant war. However, Chief's custom armor is stated as being based off an older variant of the Mark IV armor, which is the best explanation of the reason that Halsey interprets that as the Chief's new armor, which she couldn't have known about at the time since Chief was presumed MIA at the end of Halo 3 and Halsey would not have seen his custom armor.