I think there are two lines of research being confused here.
Pons and Fleischmann were working in the solid state, where the Palladium crystalline structure was trapping comparatively large numbers of Hydrogen atoms. (This high solubility is well known, and is being investigated as a safe means of H storage for fuel cells—electric cars and all that.)
The theory was that (1) The Pd structure was holding the H atoms much closer than a gaseous H would exhibit at any realizable pressure; (2) Thermal excitation—still at moderate temperatures—would drive H atoms still closer to one another, here and there, now and then; and (3) Quantum tunnelling would allow some H atoms to interpenetrate and fuse.
The other cold fusion experiments being described here utilized the cavitation of bubbles, I presume contaning H or D; I don’t think P&F were working along this line.
Bubble collapses in the cavitation process are known to produce extremely high instantaneous pressures, very localized in space and time. These, it is speculated, create opportunities for fusion.
This effect seems to me a little like the inertial confinement and laser ablation of small D-H droplets in laser fusion research, but microscopic bubbles in a liquid rather than tiny droplets in air.
Thanks for clearing that up Erasmus.
Hopefully someday we will figure out how to do some form of fusion, where we get more out of it than we put in.