What they are claiming is that hydrogen atoms inserted into a nickle lattice can be made to fuse through quantum-mechanical effect at temperatures lower than plasma. I don't see any fundamental physics violations that would necessarily bar that.
Quantum Mechanics is a Cult form of Physics that branched off of Hawking's little band of eggheads. Their problem is that they cannot prove their theory and they have retooled it so many times that even they are hopelessly confused.