Synchronization phenomena are ubiquitous processes in nature. They appear in systems as diverse as chemical reactions, peacemaker cells in the heart, Josephson Junction arrays or populations of fireflies among many other examples. In this context, phase models appear as minimal systems that capture the essence of the phenomena and are amenable to analytical study, and also as a reduced form of more complicated (and realistic) systems. In this work, we consider a system of non-identical globally coupled active rotators near the excitable regimen. We show that the system enters in a phase of synchronous firing as the diversity of the system (dispersion of the distribution of natural frequencies) is increased. This transition is found generically for any distribution with well-defined moments. Singularly, the transition is not present for the Lorentzian distribution (widely used in this context for its analytical properties). This warns about the use of Lorentzian-type distributions (and some recently proposed methods that rely on them) to understand the generic properties of coupled oscillators.