The paper you cited only deal with cell lines (i.e. in-vitro studies), whereas you can find good quality in-vivo RCT studies about both low grade inflammation and cytokines storm. Hell, you can event find meta-analysis for specific conditions and related inflammatory state (CHF, type 2 diabete, ...)

For example :

- Heart failure meta analysis: https://www.ncbi.nlm.nih.gov/pubmed/29348609 - Type 2 diabete meta analysis: https://www.ncbi.nlm.nih.gov/pubmed/29490085 - Type 2 diabete meta analysis: https://www.ncbi.nlm.nih.gov/pubmed/29945132

Hell, we even have preliminary human studies dealing with just that: clinical outcome for patients admitted in intensive care unit, with or without a single mega-dose of vitamin D: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4939707/