The capability of the thermodynamic approach based on the independent point defect approximation to describe low-temperature phase equilibria is investigated and applied to the Al-C-Fe system. The method gives a reasonable description of the multicomponent and multisublattice Fe-rich corner and evidences numerous peculiarities concerning the ordered phases as well as the density-functional-theory (DFT) energy models. The study of Fe3Al(-C), revealing strong defect-induced instabilities, rules out the LDA, SLDA and GGA schemes and leaves (spin-polarized) SGGA as the only valid one. C stabilizes L12 Fe3Al with respect to D03, which justifies the fcc-type structure of the kappa Fe3AlC compound. The present work also helps in justifying the experimentally observed depletion of C in the kappa phase. Finally, a correct description of both Fe3C and kappa requires inclusion of interstitial carbon at low temperature, emphasizing the unexpected importance of interstitial defects in ordered phases.