The article stated that Reiki can have beneficial effects and has no harmful side effects, meaning that it can be useful as a supplement to conventional medicine. This seems reasonable to me.
Beyond that, we have all sorts of people making all sorts of claims about it in the comments here. The problem, as far as I'm concerned, is if you make a claim without a shred of evidence to back it up then you are practising religion, not science.
As far as I can tell, the best anyone can offer so far are flimsy hypotheses, with very few suggestions as to how to test them. And then they try to claim this as some actual truth.
Subtle energy? It may very well be, but you can't really offer a hypothesis and then claim it as fact.
I think people would be a little more open to these ideas if those proposing them were to be more honest and say "we have no actual idea how this works, but I'm working under the hypothesis that [x] and hope that someone can come up with some way to test if this is true at some point in the future".
There are some strong claims that patients that are given more "care" recover better than those who aren't. For example, I watched a really interesting program a while ago about using the placebo effect to help people with back problems. They took a large group of people who had ongoing back troubles and told them they were giving them a new medicine to help with back pain. Half were given the medicine and half were given the placebo, except they were all given the placebo because there was no new medicine. On top of that half out of each group were given very short, brusque, medical appointments (as we are normally used to these days) and half were given longer appointments with doctors that spent time talking to them and listening to them.
Despite everyone being given a placebo, some made really dramatic recoveries, and many made at least minor improvements. And those who were cared for more seemed to make better recoveries than those who were given short appointments.
There is so much about the placebo effect and how we can heal ourselves that we do not understand even in the slightest yet.
I could give you carrots mashed in rabbit urine and swear blind that it has been proven to cure headaches. If you reluctantly took it and your headache was gone half an hour later, well maybe it would have gone anyway, maybe it went because you believed me, and maybe I got lucky and carrots mashed in rabbit urine really does cure a headache. I know where my bet would be though. (Please don't try carrots mashed in rabbits urine, I'm not even sure it would be safe for human consumption.)