Yes, I oversimplified. The Hadith (ca. 9C) was the last time anyone got any chance at *interpreting* the Koran. The shi'ites and the sunnis (pro-Hadith and anti, respectively) have been bashing hell out of each other ever since.
I guess the difference between Islam and Christianity in *this* particular sense is that there's no ongoing process of interpretation and re-interpretation of the Koran, in marked contrast to the almost-polytheistic-but-not-quite-look-ma-here's-another-sect world of Christianity.