I insist that his 2013 work, as well his 2014 work, should have been rejected on the basis of what Levi wrote in 2011, two years in advance. This makes sense, to me.
I don't recall the 2011 document. I do not think he was in charge of the experiment; he was just reporting on Rossi, in a summary fashion. In any case he had many co-authors for the 2013 work; the method and instruments were far better than previous studies; and the paper taken on its own has merit. Or at least, it seemed to have merit. You have not given a technical reason to doubt that.
As I said, I communicated with Levi and with some of his co-authors in 2013. They seemed capable to me. Subsequent events make me doubt that, but in any case my view of the paper was partly based on direct communication with the authors, which I think is a better way to judge than looking at one summary paper by one of the authors.