As Large Language Models (LLMs) increasingly mediate stigmatized health decisions, their capacity to understand complex psychological phenomena remains inadequately assessed. Can LLMs understand what we cannot say? We investigate whether LLMs coherently represent abortion stigma across cognitive, interpersonal, and structural levels. We systematically tested 627 demographically diverse personas across five leading LLMs using the validated Individual Level Abortion Stigma Scale (ILAS), examining representation at cognitive (self-judgment), interpersonal (worries about judgment and isolation), and structural (community condemnation and disclosure patterns) levels. Models fail tests of genuine understanding across all dimensions. They underestimate cognitive stigma while overestimating interpersonal stigma, introduce demographic biases assigning higher stigma to younger, less educated, and non-White personas, and treat secrecy as universal despite 36% of humans reporting openness. Most critically, models produce internal contradictions: they overestimate isolation yet predict isolated individuals are less secretive, revealing incoherent representations. These patterns show current alignment approaches ensure appropriate language but not coherent understanding across levels. This work provides empirical evidence that LLMs lack coherent understanding of psychological constructs operating across multiple dimensions. AI safety in high-stakes contexts demands new approaches to design (multilevel coherence), evaluation (continuous auditing), governance and regulation (mandatory audits, accountability, deployment restrictions), and AI literacy in domains where understanding what people cannot say determines whether support helps or harms.