Motivated by results implying that the constituents of dark matter (DM) might be collisional, we consider a cosmological (toy-) model, in which the DM itself possesses some sort of thermodynamic properties. In this case, not only can the matter content of the Universe (the baryonic component, which is tightly gravitationally-bounded to the dark one, also being included) be treated as a classical gravitating fluid of positive pressure, but, together with all its other physical characteristics, the energy of this fluid's internal motions should be taken into account as a source of the universal gravitational field. In principle, this form of energy can compensate for the extra (dark) energy, needed to compromise spatial flatness, while the post-recombination Universe remains ever-decelerating. What is more interesting, is that, at the same time (i.e., in the context of the collisional-DM approach), the theoretical curve representing the distance modulus as a function of the cosmological redshift, mu(z), fits the Hubble diagram of a multi-used sample of supernova Ia events quite accurately. A cosmological model filled with collisional DM could accommodate the majority of the currently-available observational data (including, also, those from baryon acoustic oscillations), without the need for either any dark energy (DE) or the cosmological constant. However, as we demonstrate, this is not the case for someone who, although living in a Universe filled with self-interacting DM, insists on adopting the traditional, collisionless-DM approach. From the point of view of this observer, the cosmologically-distant light-emitting sources seem to lie farther (i.e., they appear to be dimmer) than expected, while the Universe appears to be either accelerating or decelerating, depending on the value of the cosmological redshift. This picture, which, nowadays, represents the common perception in observational cosmology, acquires a more conventional interpretation within the context of the collisional-DM approach.
