The digital transformation of power distribution system has increased the demand for Distribution System State Estimation (DSSE) techniques that are robust to adversarial perturbations in addition to noise. We design a versatile method for detecting stealthy data manipulation attacks on DSSE, drawing on a model-agnostic attribution method that quantifies the contribution of each input feature to the state estimation result. The key intuition for this work is that data manipulation attacks, including adversarial and false data injection attacks, generally have a discernible effect on this feature saliency measure. Through extensive numerical simulation, we corroborate that the proposed method reliably detects various data manipulation attacks, outperforming the most prominent detection methods from the previous work.