Robust multi-label learning under noisy supervision remains a persistent challenge, where corrupted, incomplete, or ambiguous labels undermine the reliability of semantic learning. Existing approaches often address label noise through heuristic correction or local consistency constraints, but lack a unified mechanism to validate and refine supervision across structural and semantic levels. Inspired by cognitive theories of human memory, we propose CogniTrust, a novel framework that unifies verifiable supervision with a triadic memory model: episodic memory, semantic memory, and reconstructive memory. Episodic memory factorizes feature activations into spatially disentangled patterns to assess structural support and assign interpretable trust scores to labels. Building on this, semantic memory maintains class-level prototypes from structurally attentive regions to estimate semantic plausibility via prototype alignment. Moreover, reconstructive memory simulates generative supervision by interpolating between images through a diffusion-based mixup process, enriching training signals for ambiguous or borderline cases. Together, these components form a closed-loop mechanism that validates, calibrates, and synthesizes supervision from both spatial and semantic perspectives. Extensive experiments on noisy hashing benchmarks demonstrate that CogniTrust consistently outperforms state-of-the-art baselines and provides interpretable justifications for label decisions. This work establishes a cognitively grounded paradigm for denoising through structurally verifiable supervision.