There will always be people who do not have the problem, even with extreme values, just like the probability of winning the Mark Six. The chances are extremely low, but someone wins more or less every week. The problem isn't knowing whether someone will or wil not win, but exactly who and when. Probabilistic models cannot answer this latter point very well. Probabilistic models do not easily handle extreme chance scores, nor do they transfer well to other systems.
Some systems are inherently more variable than others, and some tests are more accurate than others.
This view also doesn't comfortably allow estimates of such important data as disease attack rates or the extent of treatment benefits. Disease as abnormality Statistical model relies on probabilistic approach to disease. If indicator present then disease is presumed with risk based on p. Does not easily accomodate chance results nor systems variability in Rx and outcome.