Colloidal lead halide perovskite quantum dots (QDs) exhibit size-dependent optical and electronic properties due to quantum confinement, a feature that substantiates their widespread application as classical and quantum light sources. This property is commonly characterized by photoluminescence spectroscopy, where the emission peaks blueshift with decreasing QD size. Apart from the size of the QDs, the electronic structure is strongly influenced by phonons and local disorder, being vastly different between the all-inorganic and hybrid perovskite compositions. In this study, we demonstrate that nuclear magnetic resonance (NMR) spectroscopy can serve as a powerful complementary tool to probe the local characteristics of the ground-state electronic structure. We combine optical and 207Pb NMR spectroscopy to investigate size-dependent confinement in three archetypal lead halide perovskite QDs: CsPbBr3, MAPbBr3, and FAPbBr3. While all compositions exhibit expected size-dependent photoluminescence energy, the hybrid perovskites (MAPbBr3 and FAPbBr3) display strongly reduced size-dependent confinement at room temperature when assessed via NMR. Ab initio molecular dynamics simulations suggest that this effect arises from the disorder-induced wave function modulation driven by dynamic disorder in hybrid perovskites. Experimental support for the hypothesis is provided by freezing the cation dynamics in MAPbBr3 QDs, which leads to the reappearance of the size-dependent chemical shift. By integrating local and global probes of electronic structure, our findings challenge the conventional understanding of quantum effects in soft lead halide perovskite QDs and highlight the role of disorder in shaping the local electronic structure.