Nuclear physics doesn't work this way.
High energy nuclear physics, no. All that extra energy to overcome the Coulomb barrier has to go somewhere, and moving nuclei at that speed gives them precious little interaction time.
Why is it so inconceivable that some other reaction mechanism, which keeps the nuclei in close proximity at lower energies for longer times, has different preferences for reaction pathways?
Muon-catalyzed fusion, for example, if fusion in condensed matter is so heretical. (Of course, muon-catalyzed fusion turns out to be an interesting curiousity rather than a useful power source unless and until we come up with a way of easily making muons. Fusion in condensed matter may turn out the same -- a great way to produce low grade excess heat, but not much else.)
Why assume neutrons or gammas if you don't understand what's going on? Because hot fusion tells you so? They're not talking about hot fusion, so your assumptions are bad science. Superconductivity is bad science too if you go by what happens at room temperature.