One of the papers citing the paper you linked is this paper : G. Murrieta, A. Tapia, and R. de Coss, Structural stability of carbon in the face-centered-cubic (Fm$\bar{3}$m) phase, Carbon 4, 771-774 (2004). It concludes with:
"In order to evaluate the structural stability of the fcc
phase of carbon, we have calculated the total energy as a function of the isotropic, tetragonal, and trigonal
deformations for bulk fcc carbon using the full-potential
LAPW method. We find that the total energy shows a
minimum for the isotropic deformation, but exhibits
maxima for the tetragonal and trigonal deformations.
This means that the bulk fcc structure is not a true
metastable phase of carbon. It is likely that the interaction with the substrate and impurities contribute to
stabilize the fcc structure in the existing fcc carbon thin
films on diamond. However, the exact nature of these
interactions remains unknown."
If you're interested, I would recommend further exploring the citation tree. There seems to be other studies addressing the structure and stability also from an experimental perspective.