Earthquake slip inversions aiming to retrieve kinematic rupture characteristics typically assume 1-D velocity models and a flat Earth surface. However, heterogeneous nature of the crust and presence of rough topography lead to seismic scattering and other wave propagation phenomena, introducing complex 3-D effects on ground motions. Here we investigate how the use of imprecise Green's functions - achieved by including 3-D velocity perturbations and topography - affect slip-inversion results. We create sets of synthetic seismograms, including 3-D heterogeneous Earth structure and topography, and then invert these synthetics using Green's functions computed for a horizontally layered 1-D Earth model. We apply a linear inversion, regularized by smoothing and positivity constraint, and examine in detail how smoothing effects perturb the solution. Among others, our tests and resolution analyses demonstrate how imprecise Green's functions introduce artificial slip rate multiples especially at shallow depths and that the timing of the peak slip rate is hardly affected by the chosen smoothing. The investigation is extended to recordings of the 2009 Mw6.3 L'Aquila earthquake, considering both strong motion and high-rate GPS stations. We interpret the inversion results taking into account the lessons learned from the synthetic tests. The retrieved slip model resembles previously published solutions using geodetic data, showing a large-slip asperity southeast of the hypocenter. In agreement with other studies, we find evidence for fast but subshear rupture propagation in updip direction, followed by a delayed propagation along strike. We conjecture that rupture was partially inhibited by a deep localized velocity-strengthening patch that subsequently experienced afterslip.