I’d be interested in seeing a source on that. My understanding was that it was a powerful and popular computational tool. The theory is approximate but approximate theories can still be quite useful if the approximation is a good one.
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.
I have no idea if the use of DFT here is appropriate or not.