The person who took the notes and drafts the minutes is the person who signs her work. The fact that someone else (the secretary's secretary?) may type them up for her is immaterial, as is the person who physically brings them to the meeting for approval. The person serving as secretary at the meeting where the minutes are approved (i.e. the person taking the current minutes) is the one who initials them as approved. These may be the same person or two different people and neither has to be the official "Secretary". In other words, forget titles and focus on who did what.