I think that a mathematical perspective and estimation of probabilities help, not because they are precise, but because they can guide our decision-making process. Also, they do explain human behavior to some extent. All of these notions about “reaches”, “matches”, and “safeties” are very informal ways of thinking about probabilities and utilities. If it helps to think about these concepts in a qualitative sense, then that’s fine.
I agree that the notion of “randomness” is from the perspective of the candidate, not the admissions committee, which is what I think you mean by “beyond your control”. Perhaps the word “uncertainty” is better. Even if a given admissions committee had a deterministic formula, the fact that we do not know the formula makes the probability for the candidate between 0.0 and 1.0. If we did know the formula, then we could act accordingly, and apply to a single college.
The meanings of probability and uncertainty have a long-running debate in the mathematics and statistics, ranging from a frequentist to a Bayesian interpretation. For decision making, it probably makes sense to think of probability in the Bayesian sense, which is our belief about how likely something is to occur. Given that belief, even if it is not entirely accurate, we can then act in a way that is rational or not.