Generative medical AI now appears fluent and knowledgeable enough to resemble clinical intelligence, encouraging the belief that scaling will make it safe. But clinical reasoning is not text generation. It is a responsibility-bound process under ambiguity, incomplete evidence, and longitudinal context. Even as benchmark scores rise, generation-centric systems still show behaviours incompatible with clinical deployment: premature closure, unjustified certainty, intent drift, and instability across multi-step decisions. We argue these are structural consequences of treating medicine as next-token prediction. We formalise Clinical Contextual Intelligence (CCI) as a distinct capability class required for real-world clinical use, defined by persistent context awareness, intent preservation, bounded inference, and principled deferral when evidence is insufficient. We introduce Meddollina, a governance-first clinical intelligence system designed to constrain inference before language realisation, prioritising clinical appropriateness over generative completeness. Meddollina acts as a continuous intelligence layer supporting clinical workflows while preserving clinician authority. We evaluate Meddollina using a behaviour-first regime across 16,412+ heterogeneous medical queries, benchmarking against general-purpose models, medical-tuned models, and retrieval-augmented systems. Meddollina exhibits a distinct behavioural profile: calibrated uncertainty, conservative reasoning under underspecification, stable longitudinal constraint adherence, and reduced speculative completion relative to generation-centric baselines. These results suggest deployable medical AI will not emerge from scaling alone, motivating a shift toward Continuous Clinical Intelligence, where progress is measured by clinician-aligned behaviour under uncertainty rather than fluency-driven completion.