Recent work in cross-topic argument mining attempts to learn models that generalise across topics rather than merely relying on within-topic spurious correlations. We examine the effectiveness of this approach by analysing the output of single-task and multi-task models for cross-topic argument mining, through a combination of linear approximations of their decision boundaries, manual feature grouping, challenge examples, and ablations across the input vocabulary. Surprisingly, we show that cross-topic models still rely mostly on spurious correlations and only generalise within closely related topics, e.g., a model trained only on closed-class words and a few common open-class words outperforms a state-of-the-art cross-topic model on distant target topics.