Probing studies consistently find that language models (LMs) encode the truth of a statement along a low-dimensional linear direction of the residual stream. The Truth Co-occurrence Hypothesis (TCH) (Ravfogel et al., 2025) provides a mechanistic interpretation: tracking a latent truth variable is loss-reducing because true statements co-occur with true statements in natural text, evaluated using toy models and base LLMs. We replicate and extend the toy setting. In the tested fully trainable single-layer transformers, removing truth co-occurrence while preserving fact frequency eliminates linear truth decodability, supporting the necessity of co-occurrence in this setting. However, the same manipulation leaves the original toy model largely unchanged, revealing that probe-based evidence can arise from architectural artefacts rather than a functional truth-tracking mechanism. In pretrained Llama-3.1 models (8B and 70B), we reproduce the reported behavioural effect that false context reduces confidence in true facts, but show that nearly half of the original effect is explained by surface confounds. After controlling for these confounds, the effect remains robust across six factual relations. Under our probing protocol, cross-relation performance is closer to within-relation performance at 70B than at 8B. Our work characterises the emergence conditions for linear truth representations, and highlights the limitations of probe-based interpretability studies. Reproducibility Code is available here: https://github.com/Samzmc/truth-encoding-blackboxnlp26