Very possibly, is the answer to the question that titles this post on how the diagnostic borders between mitochondrial disease and chronic fatigue syndrome (CFS) might be blurred. I bring to your attention the case report published by Fernando Galán and colleagues  (open-access available here) as an example.
Detailing the experiences of a 30-year old male who "appeared to meet the CDC-1994/Fukuda criteria for CFS [chronic fatigue syndrome]" and for whom 1 year of "cognitive behavioral therapy, graded exercise therapy, and antidepressants" resulted in only 'very slight improvement', authors eventually "considered the possibility of mitochondrial myopathy in this patient."
Screen and you may find, is the primary lesson offered by Galán et al, as "a severe deficiency of activity in complex I (nicotinamide adenine dinucleotide: ubiquinone oxidoreductase) and IV (cytochrome c oxidase) below 42% and 70% of the minimum reference of control value normalized to citrate synthase activity, respectively" is reported. Combined with several variants noted in the mitochondrial genome, and "adult-onset mitochondrial myopathy, with clinical manifestation of peripheral sensory neuropathy, autonomic symptoms, and occipital neuralgia" was the eventual diagnosis. Treatment, consisting of riboflavin (100 mg 3 times per day) and thiamine (300 mg/day) was begun, and coincided with "a marked and sustained improvement." Further clinical improvement was also noted following the use of pregabalin.
In these days of continued questioning about whether the suggested blanket psychological 'treatment' of CFS is actually cutting the scientific mustard (see here) I'm minded to reiterate how Galán et al were able to diagnose a biological reason as to potentially why this man was presenting with the symptoms he was. As far as I'm aware, cognitive behaviour therapy (CBT) is not normally indicated for treating mitochondrial disease and probably why it had such little effect in this case.
Yes this is a single case report and it would certainly be unwise to suggest that every case of CFS or ME is due to mitochondrial issues. That being said, the work from Sarah Myhill and colleagues - 'mitochondria, not hypochondria' - has been discussed before on this blog (see here). Combined with other preliminary results (see here) and I think quite a good case for screening for mitochondrial issues is being formed as and when CFS is diagnosed. Certainly following "the appearance of new symptoms and signs" one might consider putting additional screening resources in place, and indeed probably better to do said screening before any psychosomatic explanations are assumed or acted upon.
Oh, and without medical or clinical advice given or intended, the peer-reviewed literature 'around' this topic also has some other potential 'placebo-controlled' lessons to offer any interested ears (see here)...
 Galán F. et al. Mitochondrial Myopathy in Follow-up of a Patient With Chronic Fatigue Syndrome. J Investig Med High Impact Case Rep. 2015 Sep 24;3(3):2324709615607908.
Galán F, de Lavera I, Cotán D, & Sánchez-Alcázar JA (2015). Mitochondrial Myopathy in Follow-up of a Patient With Chronic Fatigue Syndrome. Journal of investigative medicine high impact case reports, 3 (3) PMID: 26904705