In direct data-driven controller tuning, a mathematical model of the plant is not needed, as the control law is directly derived from experimental data. Because the most widely used data-driven techniques are based on the assumption that the underlying dynamics - albeit unknow - is linear, the performance of the resulting controller may not be acceptable with systems whose operating region vary along the time. In this paper, we discuss how to robustify linear data-driven design by exploiting the features of scenario optimization. More specifically, we carry out a modified version of the well known virtual reference feedback tuning approach where probabilistic performance guarantees are given also when the current operating condition is diff...