The shitty thing about quantum mechanics is that you need a knowledge of vector calculus, linear algebra, differential equations, and many other uncommon mathematical concepts to understand it. Then, when you can do the mathematics, and you're actually making (correct) predictions about quantum mechanical systems, just about everyone's natural reaction is to step back and say "what the fuck is going on here?". That's the best way I can describe it, because the way things work is not reducible to English. So of course I'll make an attempt!
When the wavefunctions (akin to probability distributions - the likelihood of finding something somewhere) of particles overlap (when they are physically near each other, for instance), changes to one can affect the other. In that case, you can treat the two (or many, many, more) as a system, and the mathematics change such that strange characteristics emerge due to behavior of the collective system. One familiar result is the physics of electrical conductors and insulators. In conductors, the Fermi Level permits free movement of electrons between atoms at room temperature.
As for this possibility of transmutation? It's fair to be skeptical that any phenomenon is happening at all, with limited reproducibility, and I'm only a little less wary of this article than the new "EM microwave resonant cavity propulsion" stuff; they both seem to violate what we believe to be universal laws (conservation of energy and momentum, respectively). But since behavior at the quantum scale is so weird, people are hesitant to say that we understand exactly how or why this method of transmutation would be impossible. Personally, I'd throw more money at this than the EM-drives, but truthfully, I don't expect either to pan out. Still got my fingers crossed for both though.
And that's all I can really say about it, not much more than the article, sorry. Man, I just left my "cobbler's job", too.
Edit: So I brought this up with one of my more "nuclear-inclined" classmates for discussion. Here's the conclusion we (mostly he) came to:
The proton's rest mass is 938.2 MeV, and the electron only clocks in at 511 keV. The neutron's rest mass is 939.5 MeV; that's a +1300 keV difference compared to the proton. So for an electron + a proton, you still lack 789 keV in energy to make the neutron. That's why the article mentions requiring an electron acceleration potential of something on the order of 1 MeV to bridge the gap. This formulation is oversimplified, but the general idea is more clear than in the article (I hope).
BUT, we now know that nucleons aren't just elementary particles (like the electron and other leptons), but that there are partons comprising them. These partons (quarks and gluons) are a system of particles (like we talked about earlier) which can behave in ways we may not yet fully understand, especially when interacting with a collective group of electrons. We ended up agreeing that it was possible for an electron to interact with a parton in a way that somehow bridged this energy gap, similar to the idea of quantum tunneling. But how this process would yield a large enough amount of neutrons to transmutate enough atoms for it to be significant isn't clear.
So then we talked about applications to energy consumption. That debate is ongoing, and I'll update this thread later. Still seems to me that for this to be a worthwhile pursuit, it would violate energy conservation, and my friend doesn't disagree.