The ability to directly follow and time-resolve the rearrangement of the nuclei within molecules is a frontier of science that requires atomic spatial and few-femtosecond temporal resolutions. While laser-induced electron diffraction can meet these requirements, it was recently concluded that molecules with particular orbital symmetries (such as πg) cannot be imaged using purely backscattering electron wave packets without molecular alignment. Here, we demonstrate, in direct contradiction to these findings, that the orientation and shape of molecular orbitals presents no impediment for retrieving molecular structure with adequate sampling of the momentum transfer space. We overcome previous issues by showcasing retrieval of the structure of randomly oriented O2 and C2H2 molecules, with πg and πu symmetries, respectively, and where their ionization probabilities do not maximize along their molecular axes. While this removes a serious bottleneck for laser-induced diffraction imaging, we find unexpectedly strong backscattering contributions from low-Z atoms.