"Vitamin D treatment significantly improved fatigue in otherwise healthy persons with vitamin D deficiency."
Supplementation details, described in the paper by Albina Nowak and colleagues  (open-access available here), were a single dose of 100,000 IU [international units] of vitamin D or a placebo (mannitol) administered to 120 adult participants who presented with "fatigue and vitamin D deficiency (serum 25(OH)D < 20 μg/L)." This was a double-blind trial and self-perceived fatigue was measured using the fatigue assessment scale (FAS) at baseline (before intervention) and after 4 weeks.
This is an interesting paper but not without some issues. Use of the FAS is OK but I would have preferred to see something else accompanying the data derived from this schedule when it comes to something like self-reported fatigue. The authors did rely on a "short self-developed fatigue test (fatigue course assessment; FCA)" too during their study but I was thinking of something a little more standardised. Although data for some 120 participants were available for the study results , I was a little surprised to see that some 280 participants were initially screened for study inclusion; most of whom did not make the cut. The vast majority (n=103) were cut because "25-OH vitamin D levels >20 μg/L" or in other words, they were not classified as vitamin D deficient based on analysis by immunoassay. Bearing in mind the idea that deficiency is not the only categorisation when it comes to vitamin D and not everyone agrees where deficiency actually starts and stops, I'd perhaps have liked to have seen some more information about those excluded, particularly those on the periphery of being classified as deficient and what supplementation might have meant for them.
It's also interesting to see the strength of the placebo effect when it came to the study results as alongside the 70%+ who reported "amelioration" of fatigue who were actually in receipt of vitamin D, so half of the placebo group also registered the same/similar improvement. As far as I know mannitol is not known as a fatigue reducing agent so there's potentially something more going on here. "A significant increase in 25-OH vitamin D was observed in vitamin D but not in placebo-treated participants." Given the supplementation of vitamin D at such a high dose it's perhaps not surprising that vitamin D levels went up for those consuming the supplement.
The Nowak results do stand, and even though they were based on self-reported fatigue in an otherwise healthy cohort, I do wonder whether there may be some tie-ups with other independent study (see here for example). Accepting that there may be many reasons for fatigue, I'm also inclined to point out that for perhaps at least a subset of those diagnosed with something like chronic fatigue [syndrome], there could be some additional studies to undertake bearing in mind the authors assertion that: "our study results are not generalizable to CFS [chronic fatigue syndrome]."
To close, what if ‘There's Something About Mary’ was trailed as a Psychological Thriller?
 Nowak A. et al. Effect of vitamin D3 on self-perceived fatigue: A double-blind randomized placebo-controlled trial. Medicine (Baltimore). 2016 Dec;95(52):e5353.
Nowak A, Boesch L, Andres E, Battegay E, Hornemann T, Schmid C, Bischoff-Ferrari HA, Suter PM, & Krayenbuehl PA (2016). Effect of vitamin D3 on self-perceived fatigue: A double-blind randomized placebo-controlled trial. Medicine, 95 (52) PMID: 28033244