Language data are increasingly acquired and governed as assets, yet platforms often price candidate resources before knowing their true privacy or access costs. We study online pricing for governed language data assets under cost uncertainty. At each round, a platform observes an NLP task, a candidate asset, and a coarse cost estimate, may pay for a refined cost signal, posts a price, and receives safe net revenue. We introduce \textsc{NH-CROP}, a clipped robust pricing framework with a no-harm information-acquisition gate. The method compares direct pricing, risk-aware pricing, and verify-then-price, and acquires information only when its estimated decision value exceeds the best no-verification alternative. Across synthetic, real-proxy, and downstream-utility-grounded benchmarks, clipped \textsc{NH-CROP} variants improve or remain competitive with price-only and risk-aware baselines. Causal ablations show that paid verification is not the main source of gains in real-proxy and utility-grounded settings: the strongest learned policies often choose not to verify. Oracle and high-decision-value diagnostics show that refined cost information can still have substantial local value. Overall, governed language-data platforms should calibrate pricing under uncertain access costs first and verify only when information is cheap and decision-actionable.