Large multimodal models (LMMs) can produce fluent radiology reports, yet two clinically important error modes remain common: unsupported assertions and missed findings. Optimizing both under open supervision remains difficult because many pipelines still rely on overlapping parser families during training and evaluation. This paper introduces Truth-Anchored Dual-Extractor Counterfactual-Constrained Training (TA-DECT), which combines an ontology-derived atomic finding interface with four coupled objectives: structured prediction, dual-extractor minimax consistency on generated reports, deterministic counterfactual selectivity under evidence removal, and label-anchored completeness. In matched-path internal comparisons across chest radiographs (CheXpert, MIMIC-CXR, MIMIC-CXR-JPG) and chest computed tomography (CT; CT-RATE), TA-DECT improves truth-anchored F1 while reducing both missed-finding and unsupported-assertion rates, with concurrent gains in calibration and selectivity. On held-out region-of-interest (ROI) datasets (MS-CXR, VinDr-CXR), it also improves coarse evidence linkage and intervention-targeted confidence responses under occlusion. In this revision, the strongest claims are kept explicitly anchored to structured labels and ROI references, counterfactual evidence-sensitivity summaries are interpreted with bootstrap uncertainty, and parser-derived report metrics are retained only as supplementary diagnostics.