Your deduction is flawless, except for the fact that it doesn't disprove the Islamic interpretation. Islam holds that the text of the Bible has undergone various modifications by Christian clergies. Things have been added and deleted here and there. It's hardly any surprise that the remaining looks more like a biography.
Actually, there are many lines in the Quran that prove it wasn't written by Mohammad in person. There are prophecies and historical references and such. So a non-Muslim can question the validity of the claim that "the Quran is divinely dictated" in a similar way: it has been manipulated by others.
What remains unquestionable, is the fact that Muslims, from pagan Arabs all the way to our time, have always held Jesus and Moses in high esteem. Talking in disrespectful language about Jesus is considered as foul as doing so about Mohammad. In that regard, Muslims rarely receive mutual respect from Christians and Jews.