In emotionally supportive conversations, well-intended positivity can sometimes misfire, leading to responses that feel dismissive, minimizing, or unrealistically optimistic. We examine this phenomenon of incongruent positivity as miscalibrated expressions of positive support in both human and LLM generated responses. To this end, we collected real user-assistant dialogues from Reddit across a range of emotional intensities and generated additional responses using large language models for the same context. We categorize these conversations by intensity into two levels: Mild, which covers relationship tension and general advice, and Severe, which covers grief and anxiety conversations. This level of categorization enables a comparative analysis of how supportive responses vary across lower and higher stakes contexts. Our analysis reveals that LLMs are more prone to unrealistic positivity through dismissive and minimizing tone, particularly in high-stakes contexts. To further study the underlying dimensions of this phenomenon, we finetune LLMs on datasets with strong and weak emotional reactions. Moreover, we developed a weakly supervised multilabel classifier ensemble (DeBERTa and MentalBERT) that shows improved detection of incongruent positivity types across two sorts of concerns (Mild and Severe). Our findings shed light on the need to move beyond merely generating generic positive responses and instead study the congruent support measures to balance positive affect with emotional acknowledgment. This approach offers insights into aligning large language models with affective expectations in the online supportive dialogue, paving the way toward context-aware and trust preserving online conversation systems.