We study a systems-level visual inference problem: using an expensive privileged modality during training while preserving a fixed-cost, single-modality deployment path. We present JDCNet, a confidence-gated CT-to-X-ray distillation framework in which the CT teacher supplies an auxiliary hard or temperature-scaled target only on training samples whose teacher confidence exceeds a threshold; at deployment the student takes X-ray input alone and matches the parameter, MAC, and latency profile of the supervised X-ray baseline. On a 510-patient same-patient paired BIMCV cohort with patient-level 5-fold cross-validation, two JDCNet configurations clear a fixed transfer gate against the supervised ResNet-18 baseline: 3-slice soft-KL supervision yields $Δ\mathrm{BA}{=}{+}0.035$ ($95\%$ CI $[{+}0.011,{+}0.057]$) and mid-slice hard supervision yields $+0.033$ ($[{+}0.007,{+}0.058]$). Under the same splits and gate, logit distillation, gated logit distillation, contrastive alignment, attention transfer, feature hints, BiomedCLIP fine-tuning, and a module-augmented variant do not pass. Confidence-gated auxiliary targets are therefore a more transferable channel than uniformly softened CT logits; the evidence is bounded to one paired cohort, so external paired-cohort replication is required before any deployment claim.