The BDTMe molecule-based material is the first example of a thiazyl radical to exhibit metamagnetic behavior. Contrary to the common idea that metamagnetism occurs in low-dimensional systems, it is found that BDTMe magnetic topology consists of a complex 3D network of almost isotropic ferromagnetic spin-ladders that are coupled ferromagnetically and further connected by some weaker antiferromagnetic interactions. Calculated magnetic susceptibility xT(T) data is in agreement with experiment. Calculated M(H) data clearly show the typical sigmoidal shape of a metamagnet at temperatures below 2 K. The calculated critical field becomes more apparent in the dM/dH(H) plot, being in very good agreement with experiment. Our computational study concludes that the magnetic topology of BDTMe is preserved throughout the entire experimental range of temperatures (0-100 K). Accordingly, the ground state is the same irrespective of the temperature at which we study the BDTMe crystal. Revising the commonly accepted understanding of a metamagnet explained as ground state changing from antiferromagnetic to ferromagnetic, the Boltzmann population of the different states is here suggested to be the key concept: at 2 K the ground singlet state has more weight (24%) than at 10 K (1.5%), where excited states have an important role. Changes in the antiferromagnetic interactions that couple the ferromagnetic skeleton of BDTMe will directly affect the population of the distinct states that belong to a given magnetic topology and thus its magnetic response. Accordingly, this strategy could be valid for a wide range of bisdithiazolyl BDT-compounds whose magnetism can be tuned by means of weak antiferromagnetic interactions.