Because the Islamic scholars at the time had no axe to grind one way or the other. The Jews had good reason to dismiss him as a fraud. The Christians an equally good reason to try to make him into something he wasn't.
Always trust the independent new source more than the one with a vested interest.
And, it should be noted, his mother is more important to Islam than to Christianity. In Christianity his mother is quickly forgotten. In Islam she is a major figure.
BTW: There is essentially nothing in Christian theology that was written down at the time, nothing that hasn't been intentionally or accidentally mistranslated by the Roman Catholic and Eastern Orthodox churches. By the time anyone else saw any text it was far too late to even approximate the original. Why do you think there are so many obvious inconsistencies and contradictions?
And look at all the direct quotes? Heck no one today, even with video cameras, can remember a quote accurately 2 hours later.
