Density-functional theory (DFT) approaches have been used recently to judge the topological order of various materials despite DFT’s well-known band-gap underestimation. Use of the more accurate quasi-particle GW approach reveals few cases where DFT identifications are false positive, which can possibly misguide experimental searches for materials that are topological insulators (TIs) in DFT but not expected to be TIs in reality. We also present the case of false positives due to the incorrect choice of crystal structures and address the relevance of choice of crystal structure with respect to the ground-state one and thermodynamical instability with respect to binary competing phases. We conclude that it is necessary to consider both the correct ground-state crystal structure and the correct Hamiltonian in order to predict new TIs.