Had she come to the wrong church or at the wrong time, mistaking them for another couple? (Para. 11)
Meaning: Had she come to the wrong church or at the wrong time, thinking wrongly that they were the couple that she knew and was looking for?
mistake for: think wrongly that (someone or something) is (someone or something else)
You and your sister look so very similar, I often mistake you for her. 你和你妹妹长得很像，我常常把你当作你妹妹。