The problem is that this is either unsupported by evidence or a meaninglessly shallow claim. After all, almost every herbal remedy does something, but it doesn't mean it's actually therapeutic for some given condition.
The problem is, you’re out of date regarding the recent efforts put into studying and documenting long-known herbs.
Curcumin is a polyphenol that operates at the molecular level to disrupt multiple inflammatory cascades. It achieves this by simultaneously blocking the transcription of inflammatory genes and interrupting the enzymes responsible for generating pain and swelling.
That paper is co-authored by Bharat B. Aggarwal, who has been found to produce fraudulent research [1], and many of whose papers have been retracted. This is the guy mentioned in the New Scientist article!
Curcumin has been extensively studied, and a common observation is that it is fantastically bioactive in vitro, but tends to have zero meaningful properties when introduced into the biology of a real human being. Researchers have categorized it as an IMPS (invalid metabolic panacea), i.e. a drug whose chemical properties are an illusion, and has ended up becoming a "black hole" for scientific funding [2] [3].
The part about how it "disrupts multiple inflammatory cascades" and so on sounds terrific until you realize these are behaviours observed in vitro. The fact is that curcumin is unstable and highly reactive, so it gets torn apart and neutralized early during digestion, leading to insanely low bioavailability. Tons of compounds are anti-inflammatory in vitro. Very few actually are in the human body.
Whether it’s enough to make a difference in your case depends.