This paper critically examines the empirical evidence for the 'rough volatility' hypothesis, which claims that financial volatility follows a fractional process with Hurst exponent H<0.5. The authors propose a non-parametric, model-free estimator of path roughness based on normalized p-th variation along a sequence of partitions. This estimator is shown to consistently recover the roughness index for fractional Brownian motion and other processes. Applying the method to simulated data from stochastic volatility models, they find that even when the true instantaneous volatility has diffusive dynamics (H=0.5), the realized volatility—computed from high-frequency returns—exhibits an apparent roughness with estimated Hurst exponent significantly below 0.5. This bias persists across different values of the true Hurst exponent, suggesting that the roughness observed in empirical realized volatility series is an artefact of estimation error rather than a property of the underlying volatility process. The results imply that parametric models relying on a single Hurst parameter to capture both short-term roughness and long-term dependence are misspecified, and caution against interpreting low Hurst estimates from realized volatility as evidence for rough volatility.