Pre-trained Vision Transformers (ViTs) are increasingly deployed for medical image classification. However, correcting their inevitable failure cases in dynamic clinical scenarios poses a critical challenge. Conventional fine-tuning approaches inherently suffer from catastrophic forgetting, severely degrading previously acquired diagnostic capabilities. Such instability fundamentally compromises clinical safety. Addressing this vulnerability requires an active, controllable, and reliable intervention mechanism that is both theoretically grounded and inherently interpretable. To this end, we propose X-Edit (eXact, eXplicit, and eXplainable Editing), an efficient null-space model editing framework. X-Edit transitions the editing process from iterative gradient-based optimization to a theoretically grounded, closed-form solution. Specifically, we first explicitly localize the influential layers via causal tracing governing the erroneous prediction. Subsequently, we construct an orthogonal null-space projection matrix from a curated anchor set. By geometrically constraining the exact parameter update strictly within this null space, we provide mathematical guarantees that the intervention rectifies targeted errors without perturbing established diagnostic representations. Extensive evaluations on six medical imaging benchmarks demonstrate that X-Edit comprehensively suppresses catastrophic forgetting while achieving superior edit success rates. Our code is available at https://github.com/HenryLau7/X-Edit.