Assuming virial equilibrium and Newtonian dynamics, low-mass early-type galaxies have larger velocity dispersions than expected from the amount of baryons they contain. The conventional interpretation of this finding is that their dynamics is dominated by non-baryonic matter. However, there is also strong evidence that many low-mass early-type galaxies formed as tidal dwarf galaxies, which would contain almost no dark matter. Using an extensive catalogue of early-type galaxies, we therefore discuss how the internal dynamics of early-type galaxies in general can be understood by replacing the assumption of non-baryonic dark matter with two alternative assumptions. The first assumption is that Milgromian dynamics (i.e. MOdified Newtonian Dynamics [MOND]) is valid, which changes the effective gravitational force in the weak-field limit. The second assumption is that binary stars affect the observed line-of-sight velocity dispersions. Some moderate discrepancies between observed and predicted velocity dispersions remain also when these effects are implemented. Nevertheless, the observed velocity dispersions in early-type galaxies can then easily be explained without invoking the presence of non-baryonic dark matter in them, but with already documented variations of the galaxy-wide stellar initial mass function and non-equilibrium dynamics in some of the low-mass early-type galaxies.