When assessing relations between argumentative units (e.g., support or attack), computational systems often exploit disclosing indicators or markers that are not part of elementary argumentative units (EAUs) themselves, but are gained from their context (position in paragraph, preceding tokens, etc.). We show that this dependency is much stronger than previously assumed. In fact, we show that by completely masking the EAU text spans and only feeding information from their context, a competitive system may function even better. We argue that an argument analysis system that relies more on discourse context than the argument's content is unsafe, since it can easily be tricked. To alleviate this issue, we separate argumentative units from their context such that the system is forced to model and rely on an EAU's content. We show that the resulting classification system is more robust, and argue that such models are better suited for predicting argumentative relations across documents.