Biomedical artificial intelligence (AI) systems increasingly extract, organize, and reuse scientific claims from literature, clinical trials, and regulatory documents. But automatic extraction alone does not make a claim reliable evidence: a claim becomes useful only when it can be traced to its source, linked to the quantitative details that support it, and read within its biomedical context and uncertainty. This matters as large language models (LLMs) and increasingly autonomous systems drive evidence synthesis, knowledge graph (KG) construction, and decision support. Many text-mining and LLM pipelines remain relation-centric: they capture entities and relations such as Drug--TREATS--Disease, but drop the dose, effect size, population, comparator, uncertainty, and conditions under which a claim holds. Such relations can look actionable yet remain hard to verify, compare, or reuse. In this perspective, we argue for a shift toward quantitative evidence mining---extracting values, units, measured entities and properties, context, uncertainty, provenance, and plausibility as structured evidence units that populate evidence-aware KGs and can be checked for source grounding, unit consistency, completeness, and biological plausibility. We outline a framework for plausibility-aware AI that treats extracted claims not as final answers but as auditable evidence objects, making clear what was measured, how much it changed, in which setting, with what uncertainty, and from which source. The central risk is not only incorrect extraction, but claims that look like evidence while lacking the structure needed to trust them.

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