Doesn't the motivation itself stem from the difficulty of accepting that there are disputes about reality, because such a dispute is strange ("let them go check what the reality is"), there is no real root for the dispute, often there is no way to decide, and so on?

It isn't always so easy to check. For example, how would they check what happened in the Tabernacle (whether they moved the boards from one wagon to another through the public domain or not)? And likewise regarding assessments of human nature (back then they didn't yet conduct or know how to conduct organized surveys).

In Babylonian Talmud Bava Metzia 84a there is a nice example (in my view) on this topic:
"The sword, the knife, the dagger, the spear, the hand-sickle, and the harvest-sickle—from when do they become susceptible to impurity? From the completion of their manufacture. And when is the completion of their manufacture? Rabbi Yoḥanan said: From when they are refined in the furnace. Reish Lakish said: From when they are polished in water. He said to him: A bandit knows about his banditry."
But a bandit knows only facts.

With God's help, New Moon of Kislev 5777

Without entering into a general discussion of the question of a 'dispute about reality' —
in the case you mentioned there is no dispute about reality. It is clear that after refinement in the furnace the sword is usable, except that polishing in water improves its quality. The discussion is halakhic: what level of "finishing" is required in order to consider the sword a vessel. Is the stricter standard of a "professional" required, or is a basic level of finishing enough, one that will satisfy most people who are not professionals.

Regards, S.Z. Levinger

That really is not a dispute about reality but about the question of from when the utensil is defined as finished. The expression "a bandit knows about his banditry" is said ironically. There is no statement here that a bandit actually has understanding that determines the matter. Still, one could have said that a bandit has a more reliable sense of when the utensil is finished.

It seems strange to me to interpret it ironically when that isn't relevant, but maybe.
And I wonder about the possibility you mentioned—ostensibly, if a bandit has more reliable instincts, then the two problems with a halakhic dispute return: a. let them go check (go to bandits to benefit from their advice and insight, or do a bit of banditry for the sake of Heaven), b. one of them made a mistake (because if the title "reliable" enters the story, that implies that one opinion is definitely correct).

Levinger—obviously the substance of the dispute can, as usual, be explained as a value-based / halakhic / metaphysical dispute, and I am relying only on the expression "a bandit knows," etc.

When Rabbi Yoḥanan said to Reish Lakish, "A bandit knows about his banditry," he was hinting at his reasoning. Reish Lakish is right that by the high standards of a "professional," a sword that has not been polished is not considered finished—but in Rabbi Yoḥanan's view, the determining perspective is that of the majority of people, who do not require such a level of finishing.
Reish Lakish's "perfectionism" was expressed in the fact that he would speak only with people whose trustworthiness had been verified, to the point that they said that anyone with whom Reish Lakish was willing to speak—one could lend him money without witnesses. By contrast, Rabbi Yoḥanan would greet every person in the marketplace, even a gentile, and he even spoke with the leader of bandits, in the spirit of "love people and draw them near to the Torah."
Regards, S.Z. Levinger

Yehoshua, among the Sages there was no mentality of empirical testing. They lived with a rationalist outlook (like Aristotle), that if something is reasonable then it is true. Even the presumptions they cite were not tested in an organized survey.

What about the dispute over whether there was one frog and all the others swarmed out from it? Ostensibly that's a dispute about what reality actually was. How can it be that both are right? Likewise the dispute over whether the angels literally eat food.

First of all, who said that both are right? Beyond that, these are not disputes about reality. They are aggadic statements and parables.