Must prayers be re-offered if the order of their rakats was mistaken due to ignorance of the ruling?

Scholars have differed regarding what a latecomer (ma'mum) catches of the imam's prayer: is it considered the beginning of his prayer or the end of it? There are two opinions, and one who acts according to either of them should not be censured. The stronger opinion is that what he catches is the beginning of his prayer. This is the preferred view for two reasons: First, the narrators of "So complete it" (فأتموا) are more numerous and more accurate in their memorization. Second, "qada'" (making up) is understood in the sense of performing the action, not in its technical, jurisprudential meaning. Therefore, what the latecomer missed is the end of his prayer.