Safety-critical assistive systems that directly decode user intent from neural signals require rigorous guarantees of reliability and trust. We present GUARDIAN (Gated Uncertainty-Aware Runtime Dual Invariants), a framework for real-time neuro-symbolic verification for neural signal-controlled robotics. GUARDIAN enforces both logical safety and physiological trust by coupling confidence-calibrated brain signal decoding with symbolic goal grounding and dual-layer runtime monitoring. On the BNCI2014 motor imagery electroencephalogram (EEG) dataset with 9 subjects and 5,184 trials, the system performs at a high safety rate of 94-97% even with lightweight decoder architectures with low test accuracies (27-46%) and high ECE confidence miscalibration (0.22-0.41). We demonstrate 1.7x correct interventions in simulated noise testing versus at baseline. The monitor operates at 100Hz and sub-millisecond decision latency, making it practically viable for closed-loop neural signal-based systems. Across 21 ablation results, GUARDIAN exhibits a graduated response to signal degradation, and produces auditable traces from intent, plan to action, helping to link neural evidence to verifiable robot action.