Hyper-personalisation in healthcare aims to tailor health interventions by integrating biological, clinical, behavioural, social, environmental, and life-course data. Large language models (LLMs) are increasingly used as natural-language interfaces to access and synthesise such heterogeneous evidence, but they rely on prompt-driven interaction that shifts the burden of structuring valid health inquiry onto users with differing levels of expertise. We argue that a central limitation of LLM-enabled hyper-personalisation lies not in data availability or model capability, but in the absence of explicit support for interaction-aware inquiry design. Using an exemplar-based demonstrator across expert and lay scenarios in type 2 diabetes, we compare baseline, optimised, and interaction-aware inquiry formulations across multiple LLMs. We show that explicitly encoding interaction type, causal role, temporal framing, and evidentiary limits at the level of inquiry systematically improves the structure, calibration, and safety of AI-mediated reasoning. These findings position interaction-aware inquiry design as a model-agnostic requirement for trustworthy hyper-personalised health applications.