the deuterium nuclei are randomly inserted in the palladium lattice. There is a short-range disorder, but a long-range order:
Also Hagelstein has this fake believe. Phonon coupling is bound at the nuclear mass. But Pd has a wide variety of nuclear weights (102...110!!) so that there is absolute no chance for a higher order resonance of any significance. Aluminum is a mono isotope and much more suited for such claims.
So only electron layers can interplay and in fact inside Pd electron spin matter forms out. Unluckily current physics has no clue how electron spin matter works. Copper pairs were the first failed attempt to explain it...
Once you understand that a bound electron just contributes EM flux (and no charge) things get much more clear.