I'm not good at math. But according to your calculations, it turns out that every third person who plays against students is a cheater, and that's already paranoid.
As for mathematics, defining map hacking is essentially a probabilistic task. Because 100% proof is usually not available, one has to make assumptions with varying degrees of probability. Therefore, it is necessary to be able to work with these probabilities, at least on an intuitive level.
For me, the decisive factor is when a person chooses a questionable decision, but if they hadn't made it, they would have had a much better chance of winning the game.
And our entire dispute boils down to assigning these probabilities. That is, I argue that the probability of an honest person making such decisions is not small at all, but rather quite high.
For example, building a tower in Rampart is objectively a positive move; I indicated the reasons above. Therefore, I estimate the probability that an honest player with the appropriate skills (that is, who understands the probabilities of spellcasting) will build it there at about 70%. Another ~25 percent is left for the option of abandoning the construction in the middle and switching to building a Tavern. And another ~5% for Necropolis (a whim). A cheater, accordingly, chooses Rampart in 100% of cases.
This gives us 86% honesty against the initial 90% (assuming 10% cheaters in the group). Or, for example, 93% honesty against the initial 95% (assuming 5% cheaters). You'll agree, that's too small of an increase; such arguments need to be carefully collected in large numbers, or better yet, ignored altogether to avoid inflating the volume of the case, risking getting bogged down in irrelevant chatter.
The same is true for most of the other arguments - they each add their 1-5%, without creating a critical mass. A student, as you remember, immediately added 23%. It is such episodes that noticeably change the assessment of the situation that should be taken into account in the first place.