The correlations look fairly impressive in the plots. Then, at the end of the paper, there's this bit:
The present study analysed data from only one location, namely, one county in southern Minnesota. The short time span of the data, covering only 4–5 solar cycles, may have contributed to the weak statistics.
The authors don't propose any mechanism of how solar activity might relate to the onset of arthritis, but refer to hypotheses about melatonin secretion being affected by geomagnetic effects and/or the cloud cover. Not a word on diet, except for vitamin D deficiency, on the list of potential causes of arthritis.
I'd guess the paper might one day be used as a cautionary example of the application of statistics, if it wasn't for the volume of this sort of stuff that gets published.