I know they said that in production, and I personally find it funny, but in universe it doesn't make sense. Harry was the head of Voyager's Ops department. Being an upper-decker/bridge crew matters way more in practice than rank on paper. It's not like his department would explode oor even substantively change if he made Lt. JG.

Hell, Tuvok got promoted to Lieutenant commander in the middle of Voyager's flight and nothing weird happened in his department. And the less said about Tom Paris' rank situation the better.