That fuzziness can be quantified. It's called error bars. Whenever physicists perform a measurement, they always derive a confidence interval from the instruments they use. They take great care of accounting for the limits of each individual instrument, perform error propagation and report the uncertainty of the final result.

Consider figure 5 of the following article for example:

https://arxiv.org/abs/1105.3470

The differently shaded ellipses represent different confidence levels. For the largest ellipsis, the probability of the true values being outside of it is less than 1%. We call that 3-sigma confidence.

> Whenever I read things like "This model can't explain the bullet cluster, or X rotation curve, so it's probably wrong" my internal response is "Your underlying data sources are too fuzzy to make your model the baseline!"

Well, then do some error analysis and report your results. Give us sigmas, percentages, probabilities. Science isn't based on gut feelings, but cold hard numbers.