Style classifiers can use content cues that correlate with style labels in naturally collected data, yet we lack a systematic way to measure this reliance. We study this problem with a controlled content overlap setup built on parallel Bible translations. Specifically, we define the overlap parameter $α$ as the normalized residual of mutual information between content identity and style label, so that it measures how much content is shared across style classes: from no shared content ($α=0$) to fully shared content ($α=1$). Cross-overlap evaluation of RoBERTa-based classifiers shows that low-overlap models degrade when content cues are removed, while high-overlap models transfer more robustly. A cross-style content retrieval probe further shows that content becomes less recoverable as $α$ increases, with training dynamics showing this removal occurs gradually. Together, these results suggest that controlled overlap provides a simple diagnostic for separating style learning from content shortcuts.