So nice to meet you again on neutral ground.
Where we differ is that you hold that human category membership decisions are true-or-else-false, while I hold that they are often and typically more-or-less useful.
In your Thucydides example, his narrating an estimate of what did happen by an under- or undisclosed inclusion of what typically happens would be unacceptable by modern standards. However, it also does not make Thucydides a novelist by modern standards, either.
Modern uncertainty management recognizes that the speaker of substantive truth may employ approximation (that, after centuries of successful use of approximate reasoning in natural sciences, including the gold standard of scholarly truth-telling, physics).
Staying with your example, Thucydides narrated an approximation to the truth. That is easily distinguished both from modern historical practice (where some approximation would be allowed subject to disclosure and other conditions) and also from mainstream notions of fiction.
Pi, 3.14157, 355/113, 22/7. ..., 3.There is never a blurring.
The exact truth begins and ends with the first item. Everything else is exactly false. Nevertheless, the first few are often useful and often used. Typically, that use is without explanation or apology, nor is that needed by the "trained reader."
Is the engineer who consistently uses 355/113 for pi when that is convenient and close enough flirting with fiction? I could say that she is indulging in a falsehood (which she is), but such a statement would be misleading. I would be holding her substantially truth-respecting practice to a standard of accuracy that has no relationship with what she is trying to accomplish.
It is one use for which the approximation to the truth that Shakespeare offered is adequate. The play is convenient and close enough to accurate for the purpose stated, according to the estimation-makers named.I can't see the relevance of what undergrad students would rather study and be graded on.