The full harvesting of both singlet and triplet excitons can pave the way toward more efficient molecular light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) beyond the spin statistics limit. This TADF mechanism benefits from low (but typically positive) singlet-triplet energy gaps or Delta E-ST. Recent research has suggested the possibility of inverting the order of the energy of lowest singlet and triplet excited states, thus opening new pathways to promote light emission without any energy barrier through triplet to singlet conversion, which is systematically investigated here by means of theoretical methods. To this end, we have selected a set of heteroatom-substituted triangle-shaped molecules (or triangulenes) for which Delta E-ST < 0 is predicted. We successfully rationalize the origin of that energy inversion and the reasons for which theoretical methods might produce qualitatively inconsistent predictions depending on how they treat n-tuple excitations (e.g., the large contribution of double excitations for all of the ground and excited states involved). Unfortunately, the time-dependent density functional theory method is unable to deal with the physical effects driving this behavior, which prompted us to use more sophisticated ab initio methods here such as SA-CASSCF, SC-NEVPT2, SCS-CC2, and SCS-ADC(2).