There are several aspects of the paper of Norman Cook and Andrea Rossi that scream "amateurish": from layout to typos (hoping they're so), from historical concepts to bibliography, I'm not certainly the only one to have noted them.
But is the scientific thesis to be flawed, even without considering the disputed history of E-cat and LENR and possible prejudices one can have on the author and its reasons.
The reason is noted by the authors themselves:
...mathematical identity between the shell and lattice models have frequently been published in the physics literature, the lattice model itself has been dismissed as a “lucky” reproduction of the symmetries of the shell model.
So the article lives in the denial that an "mathematical identical" model could reach different conclusions. I have too little time and patience for a true bibliographical search, not easy since the authors are not interested in giving a reference on the above sentence (even though 5 minutes on Scholar get me on this article by Agnastatos).
The "lattice model" is long standing idea of Cook, a bit outside of basic physics consideration of the atomic nucleus (cf. Mottelson's Quantality Parameter). Moreover both Shell and Lattice Models, that are absolutely not independent particle models, but also Mean Field and Density Functional Theories, that follow an independent particle representation, are effective theories. This means that hindsight non-observables, like geometrical configurations and wavefunctions, is limited and disuputable (cf. Duguet).
What does matter are the observables, i.e. the cross section of the process, that Rossi and Cook avoid to calculate while the mathematically identical shell model, does. Carrying out properly the calculation with the lattice model, having computational and theoretical capabilities, the result would be tautologically identical, giving for author's own admission the practical impossibility of the process.