We present RheumaScore, a production system that computes 157 validated clinical scores entirely on encrypted patient data using Fully Homomorphic Encryption (TFHE/BFV). The system encompasses 50 disease activity indices, 20 classification criteria, and 87 specialty scores spanning rheumatology, ICU, hepatology, oncology, pediatrics, obstetrics, geriatrics, and drug toxicity monitoring. Deployed at rheumascore.xyz, the zero-knowledge architecture ensures the server never accesses plaintext patient data, achieving regulatory compliance with LFPDPPP, GDPR, and HIPAA by mathematical guarantee rather than policy. Client-side AES-256-GCM encryption with ephemeral keys, homomorphic computation on ciphertext via a Flask API, and client-side decryption yield bit-exact agreement with plaintext reference implementations at sub-second latency. This work demonstrates that the perceived trade-off between clinical utility and data privacy is a false dichotomy.