There may also be an objection with respect to Tungsten, since the BECNF is about Ni H systems, not tungsten.
What caught my attention, besides the phonon reference was this quote near the end:
This is an important dissipation channel for energy and will affect chemical reactions at surfaces, such as reactions on catalysts. Another interesting implication is the possibility of an electron-phonon-mediated superconductivity that is confined to the surfaces of metals and has a greatly enhanced critical temperature as compared to ordinary superconductors. [emphasis added]
As I noted before, "cold fusion" has been said to be a surface effect phenomenon.
A closer look at this paper allows another quote that I find interesting:
Since these "many-body" effects are often more prominent in physical systems with less than three dimensions [ comment: as you would find on the surface] carefully prepared surfaces furnish good two-dimensional test beds for examining these effects in detail.BCEs in this context probably qualify as a type of "many-body" effects referred to here.
Rossi's catalyst then, could be key. Maybe that is why it is such a big secret.