In order to prove an historical event, the account must contain two elements; 1) The presence of masses, and 2) Clear facts. Masses removes the possibility that a given story was fabricated. Mass conspiracy is against human nature. No group of people can all share equal motivation to lie, thereby perpetuating a fallacy. Motive is a very subjective phenomena. If we ever find a case in history attended by masses, we know there was no fabrication.
But you might ask, "Perhaps we possess a story with masses, and although masses proves there was no purposeful distortion (fabrication) yet, might I still claim that the attendants of this event erred in their perception? Cannot distortion take place not only willfully through fabrication, but via ignorance of the viewers?"
My response is, this is why we also require "simple phenomena", to disprove any possibility of ignorance. If we demonstrate that a given event contained elements easily apprehended, there is no reason to assume ignorance. Once we demonstrate the story under discussion contained no willful or accidental distortion, the story must be true. There are only these two possibilities why a communicated story can be false; 1) Either it was purposefully fabricated, or 2) it was not clearly communicated.
Going back to our case of JFK, we see there were both, masses and simple phenomena which any individual understands with 100% accuracy. But ask people which angle the bullet entered JFK's head, and now we enter an area where the phenomena is not clearly observable, and we find debate. But on he fact that JFK was shot, and on a certain date and location, there is no debate at all.
Sinai also contains these two elements, 1) There were over 2 million people present, proving there was no fabrication, and 2) the event was easily apprehended: All people know what a mountain is, what fire is, and that they heard words emanating from the fire. Not so regarding Jesus's stories. We find no masses at any of his proposed events of miracles, just a description of smaller groups, wherein lies can take place.We therefore do not accept these stories as truths.
The stories of Jesus' miracles are missing the first - there are no masses, just a proposed small group. But Moses ascending to Mount Sinai, and the Jews hearing intelligent words from the mountain amidst the flames were witnessed by millions.
Based on such credibility, we state with conviction that the event at Mount Sinai must have occurred. Otherwise, history would not be spread in the form of factual events. Christianity is not based on an event where great numbers attested to an event. No religion other than Judaism makes this claim, as no other religion or people witnessed such a miracle en masse.
It is also important to note that there are no alternative histories recorded of the Jews at that time. All Jews today trace back their lineage to that event, without fail. Had Sinai never occurred, it would be impossible for Moses to perpetuate such a lie, making masses believe they were at an event - when they weren't. It is impossible.
Using scientific reasoning, we conclude, the only religion claiming God's validation is Judaism. No other religion contains any proof whatsoever.
Your other question, whether there is a distinction that Jesus's stories make claim to his miracle performances independent of God, may be how Christians view Jesus. But this is of no concern. As we have disproven any such story in general, the details are also disproven.