Falsifiable Claim–Region Grounding in 3D CT

3D CT grounding usually evaluates where a supported finding is located, while verification evaluates whether a claim matches a scan. These separate tests miss a failure in which a real finding is displayed as support for a false claim. If a CT shows a finding in the left lower lobe but the claim places it in the left upper lobe, the finding is real yet does not support that claim. Positive-only grounding may still return its region, whereas a global verifier may reject the sentence without identifying the conflicting region. This paper introduces ReX-Verify, which keeps the CT and annotated source region fixed as location and finding edits change that region from support to annotation-relative counter evidence. The accompanying Claim-conditioned Evidence Grounding for Verification (CEG-Verify) model predicts separate support and counter fields, suppresses support for non-supported claims, and uses the predicted relation to select the returned field. Matched comparisons show that false-support supervision reduces exposed support after relation errors, mainly for cross-case unsupported claims, while also reducing returned maps for supported claims. Outcome decomposition attributes the reduction to map blocking after false admission. Exact-text and region analyses show weak image-conditioned discrimination and coarse counter localization.