Recent advances in reasoning-oriented Large Language Models (LLMs) have been driven by the introduction of Chain-of-Thought (CoT) traces, where models generate intermediate reasoning traces before producing an answer. These traces, as in DeepSeek R1, are not only used to guide model inference but also serve as supervision signals for Knowledge Distillation (KD) to improve smaller models. A prevailing but under-examined implicit assumption is that these CoT traces when emitted at inference time are both semantically correct and interpretable for the end-users. While there are reasons to believe that these intermediate tokens help improve solution accuracy, in this work, we question their validity (semantic correctness) and interpretability to the end user. To isolate the effect of trace semantics, we design experiments in the Question Answering (QA) domain using a rule-based problem decomposition method. This enables us to create Supervised Fine-Tuning (SFT) datasets for LLMs where - each QA problem is paired with either verifiably correct or incorrect CoT traces, while always providing the correct final solution. Trace correctness at inference time is then evaluated by checking the accuracy of every sub-step in decomposed reasoning chains. To assess end-user interpretability, we finetune LLMs with three additional types of CoT traces: R1 traces, R1 trace summaries, and post-hoc explanations of R1 traces. We further conduct a human-subject study with 100 participants asking them to rate the interpretability of each trace type on a standardized Likert scale. Our experiments reveal two key findings - (1) CoT trace correctness is not reliably correlated with the model’s generation of correct final answers: correct traces led to correct solutions only for 28% test-set problems while incorrect traces don’t necessarily degrade solution accuracy. (2) In end-user interpretability studies, fine-tuning on verbose R1 traces produced the best model performance but these traces were rated as least interpretable by users, scoring on average 3.39 for interpretability and 4.59 for cognitive load metrics on a 5-point Likert scale. In contrast, the decomposed traces that are judged significantly more interpretable don’t lead to comparable solution accuracy. Together, these findings challenge the assumption in question suggesting that researchers and practitioners should decouple model supervision objectives from end-user-facing trace design.