The LBNL DFT paper isn't claiming to have modeled the strong correlations. Rather, they observe a specific feature of the band structure (flat bands crossing the Fermi level formed from d-orbitals) that have also appeared in DFT calculations of other high-temp superconductors and are considered a signature of those materials. In the other high-Tc materials, the calculations are consistent with experiment, and so the unexpected appearance of these bands in the reported crystal structure is seen as a signal of "hey, if this turns out to be real, we can explain it with current physics." That's something that previous fraudulent claims of room temperature ambient pressure superconductors (University of Rochester group) couldn't do.
The other interesting conclusion of the LBNL paper is that the low-energy physics of the electronic structure can be effectively modeled by a two-level effective Hamiltonian. This is a common pathway to bridging the gap between DFT calculations and theoretical understanding of strong correlations.
None of the serious scientists are saying "hey, look, DFT predicted it so it's true." Rather, it doesn't rule it out, and it suggests that it could be understood with our current physics. That's significant in itself.
The other interesting conclusion of the LBNL paper is that the low-energy physics of the electronic structure can be effectively modeled by a two-level effective Hamiltonian. This is a common pathway to bridging the gap between DFT calculations and theoretical understanding of strong correlations.
None of the serious scientists are saying "hey, look, DFT predicted it so it's true." Rather, it doesn't rule it out, and it suggests that it could be understood with our current physics. That's significant in itself.