The arXiv paper 2605.27567 establishes that supervised fine-tuning, DPO and in-context learning produce predictors unable to separate causal graphs yielding equivalent observational distributions. On Corr2Cause, A-CBO matches fine-tuned baselines; on the 24-variable Extended Corr2Cause benchmark it outperforms them with the gap widening as node count grows. The limitation is formalized as requiring unbounded representation growth, violating conditions of the training methods themselves. The kernel obstruction applies across model scales and datasets rather than any single architecture. Related results on observational equivalence in causal discovery (Spirtes et al., 2000) confirm that passive data alone cannot resolve Markov equivalence classes. A-CBO routes queries through an external Bayesian loop that treats the frozen LLM solely as an interventional oracle, concentrating posterior mass over graphs in logarithmic rounds. This separation places decision-making outside the obstructed predictor space.