But that just isn't the way science works. That's why a probabilistic way of viewing it makes more sense than simple falsification. No serious theory in science

But that just isn't the way science works. That's why a probabilistic way of viewing it makes more sense than simple falsification. No serious theory in science is ever going to be overturned with "just one test". At most, one's estimate of the theory's truth is going to be slightly reduced when a counterexample is found, as every scientific theory is just a model of the world, and obviously can't cover every minor exception. If it turns out that many exceptions are found, then yes, the theory has a problem and needs to be fixed.