If the energy of each atom is below a threshold level, they all bounce off one another due to electromagnetic forces. If any collide forcefully enough, they can penetrate the repulsion of the EM, down to the distance at which the attractive nuclear forces outweigh the EM repulsion. Then you get a net energy release, because the fused nuclei are a lower rest energy state (marginally lower mass) than seperated.
So, the hard to believe part is the claim that they have found a way to get a fairly high portion of the available macro force, to dump into a relatively small portion of the atom population. That is what they claim the ultrasound and collapsing bubbles are doing. Imagine a "spectrum" of the "temperatures" of individual atoms. They want a long "tail" at the high energy end. Most moving slowly, a few moving very fast.
Whether it is true, I don't pretend to know. Of course on its face it is not very likely. It is at least as likely that they just measured the energy budget incorrectly, and no energy release from fusion was going on. (E.g. if they measured the energy input from the ultrasound just slightly wrong, it could look like a net energy release was occurring, when it wasn't).
It is also possible, even if they are right in their claims, that only a tiny portion of the atoms can be pushed to high enough energies in the manner they found, with the result being the whole thing can't scale up to any meaningful macroscopic energy source. In that case it would still be of theoretical interest, but not anything directly practical.