Our Gemara on Amud Aleph discusses the legal disposition of two sets of witnesses who cancel each other out, essentially, mutually discrediting the other’s testimony. The reasoning is as follows: Since at least one of them must be lying, thereby due to the conservative nature of law, we cast a shadow of doubt on the legitimacy of both testimonies.
Malbim (Bamidbar 16:28) uses this legal distinction to explain Moshe’s atypical response to the Korach rebellion. Moshe’s usual stance was to pray for the sinners, even when he had scoffers who doubted his leadership and authority, or literally, the direction they were heading. But the Korach rebellion went beyond the insubordination and disobedience of the other insurrections, this one challenged the validity of Moshe’s revelation at Mount Sinai. Malbim argued this was more undermining than previous uprisings amongst the people. Until now, there was valid uncontested testimony of an entire Nation witnessing the revelation of the Torah on Mount Sinai. But now, Korach and company were making a contradictory attestation, that perhaps, (God forbid!), Moshe fabricated parts of the Torah. Moshe’s prior testimony was potentially invalidated by Korach and company’s contradictory testimony. This is why Moshe was insistent that Hashem show them no mercy and produce a unique and miraculous action to re-establish Moshe’s legitimacy as prophet (ibid, 29-30):
And Moses said, “By this you shall know that it was Hashem who sent me to do all these things; that they are not of my own devising:
if these people’s death is that of all humankind, if their lot is humankind’s common fate, it was not Hashem who sent me.
But if Hashem brings about something unheard-of, so that the ground opens its mouth and swallows them up with all that belongs to them, and they go down alive into Sheol, you shall know that those involved have spurned Hashem.
This idea that a tradition of an entire nation who witnessed an event offers incontrovertible evidence of its validity, is also known as the Kuzari Principle. The Kuzari argued that other religions rely on a prophet who brings back word from God, at best with a miraculous sign and witnessed by a local group. However, the Jewish tradition has the audacity to assert that an entire nation simultaneously witnessed a miraculous event. Surely this constitutes compelling evidence, as wouldn’t the people of the time object to the bizarre claims of the prophet! (See Kuzari Book 1:9-80. But actually I believe this proof was first articulated by Rav Saadia Gaon in Emunos V’Deos, Book 3:4-5.)
To be intellectually honest, the proof never sat so well with me, as modern historical analysis has argued about other groups and tribal histories, a legend can grow gradually over time. We can argue that the legend started with a core story and then, out of national or religious pride, continued to become more grand and embellished. This is a legitimate argument, knowing how groups of people behave and stories evolve.
Before y’all call me an apikores, no proof is good if it isn’t subject to honest evaluation and criticism. In the field of Jewish philosophy, the Rambam, Chovos Halevavos, Rav Saadiah and Sefer Haikkarim each robustly debate and critique various religious proofs, holding them to the highest logical standards, and rejecting those that fall short. Furthermore, the Malbim’s account we just saw actually describes Korach undermining the Kuzari Principle. Granted, Moshe’s legitimacy was re-established via the new miracle of the hole in the earth which swallowed Korach and his men, but it did not necessarily show that the public witnessing of Mount Sinai was uncontested, since indeed Korach did successfully object. Notably, the recorded response wasn’t condemnation from the other people, saying his claims were absurd. Rather, Moshe had to produce a new miracle to prove his point. This suggests, that neither Moshe nor the Jewish people were not much swayed by the strength of the Kuzari Principle. Where were those Jews who objected to Korach, saying, “But we all saw it and we all were there!” I should note, all of this is only according to Malbim’s account of Korach’s claims. A pashut peshat interpretation of Korach’s claims does not undermine the Kuzari Principle, because Korach was merely arguing why Moshe and Aharon had to be the leaders; not an outright rejection of the Sinai Revelation.
In the final analysis, we can still recognize that the Jewish tradition of a mass revelation on that scale seems to be unique in religion, and I think it is a compelling argument, but as we see, not necessarily a foolproof one. However, a refutation to a proof is not a refutation to a fact. One can still believe in the truth of the Torah for all kinds of reasons, including a tradition, personal feeling of its rightness and a collection of numerous persuasive arguments, without agreeing to proofs that might not seem as compelling over the sands of time.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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