Where or that

¦ The unprepared northern tribes fled to places where Qin's army could not reach. (FYI: The sentence was written by someone who is not a native speaker.) I think the relative adverb where or which should not be there because the act of army's reaching was not taking place in places, the underlined word. Instead that should be there because the clause Qin's army could not reach is modifying places only, not like the army is reaching places in that same places, which is impossible. But I am still not sure if I should put that instead of where. Could you help me clarify it? Thanks.