Reentrant layer-by-layer growth is studied using a Monte Carlo simulation of a solid-on-solid model. A previously proposed explanation of the phenomenon based on the existence of an activation barrier for adatom hops off descending steps has been used to reproduce correctly most of the available experimental data. However, based on a detailed inspection of the growth kinetics, we propose a different interpretation of the origin of low-temperature layer-by-layer growth, which stresses the importance of the incorporation mechanism of an atom arriving on the surface.