In the study, a group of people with MS were put on a diet that matches up with most diets that are labeled "anti-inflammatory." The article reads: subjects were put on "a calorie-restricted, semi-vegetarian diet and administration of vitamin D and other dietary supplements (fish oil, lipoic acid, omega-3 polyunsaturated fatty acids, resveratrol and multivitamin complex)."
The problem with the study, which is the problem with most medical studies, is that it was too short. The people were only studied for months, not years, and you just have to look to Swank's data (reported in Jalinek's book) to see that diet only really started to reduce exacerbations after years, not months.
But what did the study find? In just a few months, there were no measurable neurological changes. No surprise there. However, the diet did register as anti-inflammatory, reducing apparent markers of inflammation in their systems. In the words of the 11 authors: "serum levels of the activated isoforms of gelatinase matrix metalloproteinase-9 decreased by 59% in primary-progressive multiple sclerosis and by 51% in relapsing-remitting multiple sclerosis patients under nutritional intervention." So there were immediate consequences of following the diet, just not (yet) consequences of neurological magnitude.
Riccio et al. 2016, March. "Anti-inflammatory nutritional intervention in patients with relapsing-remitting and primary-progressive multiple sclerosis: A pilot study," Experimental Biology and Medicine, pp. 620-635, doi: 10.1177/1535370215618462