Recent works show that LLM agents struggle to correct errors in their own reasoning traces, despite their ability to correct errors from external sources. We ask whether this reflects a capability deficit or an artifact of the role labeling. To test this, we design a training-free intervention, source-conditioned role relabeling, that keeps the erroneous claim byte-identical and varies only its message role. The claim is presented inside the agent's "<thought>", a user message, a tool response, or a system "<memory>" block. We test 12 model-domain combinations spanning closed-weight APIs and open-weight models from 70B-class down to smaller families. Relabeling "<thought>" to an external role increases the explicit-correction rate by 23 to 93 percentage points, significant in 10 of 12 experimental settings. This suggests that these models' failure to detect a self-generated error is largely an artifact of how the claim is role-labeled in the chat template, rather than a pure cognitive deficit. The most effective role label is domain-dependent: "<memory>" dominates in most math experiments, while a user message dominates in logical deduction. Recognizing role-label handling as a key experimental variable in instruction tuning presents a more direct path to closing the self-correction gap.d

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