Remote health monitoring BASNs promise substantive improvements in the quality of healthcare by providing access to diagnostically rich patient data in real-time. However, adoption is hindered by the threat of compromise of the diagnostic quality of the data by faults. Simultaneously, unresolved issues exist with the secure sharing of the sensitive medical data measured by automated BASNs, stemming from the need to provide the data owner (BASN user / patient) and the data consumers (healthcare providers, insurance companies, medical research facilities) secure control over the medical data as it is shared. We address these issues with a robust watermarking approach constrained to leave primary data semantic metrics unaffected and secondary metrics affected minimally. Further, the approach is coordinated with a fault tolerant sensor partitioning technique to afford high semantic accuracy together with recovery of biosignal semantics in the presence of sensor faults, while preserving the robustness of the watermark so that it is not easily corrupted, recovered or spoofed by malicious data consumers. Based on experimentally collected datasets from a gait-stability monitoring BASN, we show that our watermarking technique can robustly and effectively embed up to 1000 bit watermarks under these constraints.