The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.