The complex photoisomerization mechanism of the dihydropyrene (DHP) photochromic system is revisited using spin-flip time-dependent density functional theory (SF-TD-DFT). The photoinduced ring-opening reaction of DHP into its cyclophanediene isomer involves multiple coupled electronic states of different character. A balanced treatment of both static and dynamic electron correlations is required to determine both the photophysical and photochemical paths in this system. The present results provide a refinement of the mechanistic picture provided in a previous complete active space self-consistent field plus second-order perturbation theory (CASPT2//CASSCF) study based on geometry optimizations at the CASSCF level. In particular, the nature of the conical intersection playing the central role of the photochemical funnel is different. While at the CASSCF level, the crossing with the ground state involves a covalent doubly excited state leading to a three-electron/three-center bond conical intersection, SF-TD-DFT predicts a crossing between the ground state and a zwitterionic state. These results are supported by multi-state CASPT2 calculations. This study illustrates the importance of optimizing conical intersections at a sufficiently correlated level of theory to describe a photochemical path involving crossings between covalent and ionic states.