Most clinical AI systems operate as prediction engines -- producing labels or risk scores -- yet real clinical reasoning is a time-bounded, sequential control problem under uncertainty. Clinicians interleave information gathering with irreversible actions, guided by regret, constraints and patient values. We argue that the dominant computational substrate of clinician reasoning is not cardinal optimization but ordinal, non-compensatory decision-making: Clinicians frequently rely on fast-and-frugal, lexicographic heuristics (e.g., fast-and-frugal trees) that stop early after checking a small, fixed sequence of cues. We provide a normative rationale for why such algorithms are not merely bounded rationality shortcuts, but can be epistemically preferred in medicine. First, many clinical trade-offs are constructed through human judgment and are only weakly measurable on absolute scales; without strong measurement axioms, only orderings are invariant, motivating an ordinal-by-default stance. Second, preference and signal elicitation are structurally crude: The mapping from truth $\to$ perception $\to$ inference $\to$ recorded variables introduces layered noise, leaving a persistent uncertainty floor. When this 'crudeness' overwhelms the decision margin, plug-in expected-utility optimization becomes brittle (high flip probability under small perturbations), whereas robust dominance/filtering rules ($ε$-dominance, maximin) stabilize decisions.Finally, we outline a clinician-aligned AI blueprint: Use rich models for beliefs and trajectories, but choose actions through robust ordinal rules; treat heuristics as the low-dimensional special case; and deploy AI as 'selective complexity' -- invoked mainly for tie-breaking when decisions are fragile and information has positive expected impact.