Every religion has rhetorical arguments for various purposes and National Revelation at best is rhetoric. If taken as a logical argument, it melts down pretty easily
1) IF there was a national revelation, what proof do you have that it was God's? "Cacodaemony," is an interesting essay by Steven M. Cohn, wherein he demonstrates logically how an omnimalevolent, omnipotent Demon could create goodness in the world. Can it be logically proven that the revelation on Mount Sinai was NOT a powerful Cacodemon at work? What defense do you have against an allegation that it was a Jinn, a demon, or Azazel himself who deceived an entire nation?
2) It was magic! Which is by far the most common retort hurled toward Messengers of God, including Muhammad (pbuh). We know Moses (pbuh) could convert a wooden staff into a mighty serpent - that's powerful. Surely must be trivial to fake God's voice?
3) IF there was a national revelation, it was the only such event in history, and exactly how many divinely inspired books of the Tanakh were written by later Prophets? How many men claimed to have revelations, visions, inspirations of Divine origin AND ** were accepted as people of Book? ** What made those revelations reliable? The Rabbi's argument can be fitted to every Prophet after Moses (pbuh).
4) The NR-argument held against Christianity and Islam is a fallacy, it does not follow logically that a single man can NEVER have a true revelation.
My last point is my answer to your question "why take the Prophet Mohammad at his word?": Because even a single person can speak the Truth!
"How is it known that he is not making it up?"
Based on inherited or acquired faith and personal conviction, which works differently for different people! Such is the nature of faith, no one else can cook it for you. After all, from a philosophical point of view, the argument that we might be living in a Cacodaemony retorts all "known" faiths.