A set of high resolution zero-degree inelastic proton scattering data on 24Mg, 28Si, 32S, and 40Ca provides new insight into the long-standing puzzle of the origin of fragmentation of the Giant Dipole Resonance (GDR) in sd-shell nuclei. Understanding is provided by state-of-the-art theoretical Random Phase Approximation (RPA) calculatios for deformed nuclei using for the first time a realistic nucleon-nucleon interaction derived from the Argonne V18 potential with the unitary correlation operator method and supplemented by a phenomenological three-nucleon contact interaction. A wavelet analysis allows to extract significant scales both in the data and calculations characterizing the fine structure of the GDR. The fair agreement supports that the fine structure arises from ground-state deformation driven by alpha clustering.