It would have been nice to know what Dog Person's operational definition of ME/CFS is. To really study a population, you need to define that population. When researchers study ME/CFS, they accept participants on the basis of a defined sample. Results need to be compared to another population. If Dog Person finds that a mineral level is off in the hair analyses she obtained from members, she can't really conclude much if she doesn't define a cohort and include a comparision to a "normal" population.
I think a huge question needs to be addressed here. Are the symptoms of ME/CFS due to inadequate nutrition or are the symptoms of ME/CFS due to the illness process rather than to inadequate nutrition? Then another question to answer, if people with ME/CFS have a consistent deficiency over the population, how much does the deficiency contribute to symptoms. Then one has to consider modifiable versus non-modifiable risk factors. We can modify our diets, so the necessary question is, does the population being studied here have the same dietary intake -- are they eating a healthy diet, a processed diet, a diet with no additives. We can modify health habits. Then you have to look at underlying disorders. Does the population have normal kidney function, normal/abnormal absorption of nutrients etc. Then there are environmental factors, does the population live in areas with lots of pollution or in a less polluted environment, are they exposed to mold etc. Do they drink water supplied by their city (which varies vastly in mineral/lead etc content, or do they drink mineral water. How much stress is the population under. Then you have to consider non-modifiable factors -- gender, genetics etc. Basically, there are a huge number of factors to consider before making any conclusions.
I wonder why there is a huge number of people out there that eat crap everyday, day in, day out, and feel fine. If our illness is down to some nutritional imbalance, why are we affected so badly, when others aren't. I remember when I was at University. My diet was awful. Junk food, lots of parties, no sleep, huge stress and I felt just fine. I later changed my diet and lifestyle radically, I exercised and probably did have more energy to do things. I eat better than anybody I know in my small social life, yet I am so ill. So a nutritional cause really doesn't make sense to me unless my body just isn't using the nutrition like it used to. If that's the case, any more improvements won't be helpful until any underlying cause is identified.
There are many unanswered questions here and I hope that Dog Person considers some of these issues while she is developing her hypothesis. This thread has provided lots of food for thought.