Another error you have there and your terminology is also incorrect. In general relativity the notion is quantitative, not arbitrary. The local curvature scale is set by the Riemann tensor, roughly a radius of curvature. In any region of which size is much smaller than that scale, deviations from flat Minkowski geometry fall as higher order terms and can be made arbitrarily small simply by shrinking the region. That is a controlled approximation, not an arbitrary cutoff. In other words, negligible has a precise operational meaning, the error can be reduced below any chosen tolerance by restricting attention to a sufficiently small neighborhood. This puts you Lightyears behind of understanding what it is that you’re trying to reconcile with.
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