Reconfigurable Intelligent Surfaces (RISs) are announced as a truly transformative technology, capable of smartly shaping wireless environments to optimize next-generation communication networks. Among their numerous foreseen applications, Reflective RISs (RRISs) have been shown theoretically beneficial not only to enable wireless localization through controlled multipath in situations where conventional systems would fail (e.g., with too few available base stations (BSs) and/or under radio blockages) but also to locally boost accuracy on demand (typically, in regions close to the surface). In this paper, leveraging a dedicated frequency-domain mmWave indoor channel sounding campaign, we present the first experimental evidences of such benefits, by emulating offline simple RIS-aided single-BS positioning scenarios including line-of-sight (LoS) and non-line-of-sight (NLoS), single-RIS and multi-RIS, and multiple user equipment (UE) locations, also by considering various combinations of estimated multipath parameters (e.g., delays, Angle of Departure (AoD) or gains) as inputs to basic Least Squares (LS) solvers. Despite their simplicity, these preliminary proof-of-concept validations show concretely how and when RIS-reflected paths could contribute to enhance localization performance.