This study specifically
excluded people with pre-existing diverticular disease (if known). Nobody has been recommending exclusion of such foods from all diets. The authors of this study have attempted to say that since eating these things didn't cause diverticular disease, that it's okay with people with diverticular disease to eat these foods. They have drawn conclusions which their study was not designed to evaluate.
It is entirely possible, for example, that the reason that they saw an inverse relationship was that those foods might reflect a healthy, fiber-rich diet and hence might contribute to healthy colonic motility, thus preventing the development of diverticula in the first place. Those who developed diverticulOSIS for some other reason might have developed diverticulITIS by getting a nut, seed or bit of corn lodged in a diverticulum. They did not comment on the contents of the diverticula that got inflamed.
A much more appropriate study, in my mind, would be the same evaluation on a series of patients who DO have a history of diverticulosis, because the question is not whether or not such foods
cause diverticula, it's whether or not they
irritate/erode/perforate diverticula when they get stuck.
Just my $0.02, of course.

-- David