Unauthorized distillation turns reasoning traces into a conduit for transferring proprietary models’ reasoning behavior to smaller students. Antidistillation Sampling (ADS) perturbs decoding to preserve task utility for legitimate users while obstructing student imitation. Our token-level Metropolis–Hastings diagnosis reveals that current ADS-style defenses leave the trace’s intrinsic learnability largely intact: most tokens still follow the original teacher, while a few teacher-uncertain positions induce extreme loss and dominate optimization. ADS hides learnable reasoning behind a sparse high-loss tail instead of eliminating it. We therefore reformulate reasoning distillation as offline reinforcement learning from imperfect demonstrations, with credit assignment that reinforces high-quality reasoning behavior while suppressing disruptive segments. Across two teachers, six students, and six datasets, the resulting learner extracts reasoning from current anti-distillation traces, outperforming vanilla maximum-likelihood training and eight supervised fine-tuning baselines by up to 21%. We then turn the same principle into an adaptive defense that directly targets high-value reasoning behaviors, exploiting the perceptual gap between humans and models to preserve readability while disrupting model-visible Unicode sequences. This strategy sharply degrades both classical distillation and the adaptive learner, and scales to protect GPT-5.5 traces. These results suggest that robust anti-distillation should optimize for low intrinsic learnability, not merely high token-level surprise.