Large language models increasingly answer health questions in settings where the timing and specificity of guidance may matter, yet many safety evaluations reduce responses to whether a recommended action eventually appears. We tested whether minimal relationship wording changes emergency guidance and whether increasingly decisive supplied emergency evidence constrains those differences. Across three preregistered experiments, GPT-5.6 Terra and Claude Sonnet 5 produced 24,000 cold, single-turn responses under three system-prompt conditions. In Study 1 (N = 2,880), explicit unresponsiveness raised explicit emergency-medical-services (EMS) directives from 48.19% to 100% overall; under the weaker prompt, EMS rates differed substantially by relationship term. Exploratory response-position differences beneath the emergency ceiling motivated a prospective positional endpoint. Study 2 (N = 5,760) replicated that foregrounding effect across eight matched relationship terms: every explicit-emergency response contained an EMS directive, but mean first-directive position ranged from 9.99 to 24.95 words across referents, and female-coded versus male-coded differences reversed direction across relational roles. Study 3 (N = 15,360) crossed the same referents with four evidence levels and two wording variants. EMS presence was 97.60% overall and relationship-dependent chiefly for Claude under responsive impairment; wording variants also produced large Level-1 shifts. Conditional relationship spreads in first-directive position contracted from 29.79 to 0 words across the evidence ladder for GPT and from 79.96 to 1.39 words for Claude. Existing post-confirmatory descriptive checks further showed that many Claude responses without an explicit EMS directive still contained generic help-seeking or warning guidance, narrowing the low-evidence interpretation from help versus no help to escalation specificity. A preregistered discourse classifier failed prospective human validation and was excluded from substantive inference. Together, the studies show that relationship cues can shape an observable emergency-response policy under ambiguity, while stronger task-relevant evidence sharply constrains variation on the measured emergency-response dimensions. ( direct link )