Reconfigurable intelligent surfaces (RISs) are electromagnetically passive controllable structures, deflecting the incident wave beam in directions predefined by the control signal. A usual way to design RIS based on metasurfaces (MSs) is based on the application of the approximation in which the reflective properties of a uniform MS are attributed to a unit cell of the non-uniform one. We call this approximation the reflection locality. In the present paper, we show that this approximation may result in heavy errors. We also find a condition under which this approximation is applicable for a wide range of incidence and deflection angles. This condition is the angular stability of the reflection phase of a uniform MS based on which the non-uniform one is generated. We present an approximate analytical proof of the equivalence of the reflection locality and angular stability. As an example, we report theoretical and experimental results we obtained for a binary RIS whose generic uniform analogue has the angular stability. Meanwhile, for its counterpart without angular stability (the so-called mushroom MS) the same model fails.