I don't have paid access, so couldn't find out about that one. However, I did check a few other papers the lead researcher has co-authored.
Postprandial effect of n–3 polyunsaturated fatty acids on apolipoprotein B–containing lipoproteins and vascular reactivity in type 2 diabetes. Part funded by Ross Products Division, Abbott Labs. Abbott Labs is a big pharma and Ross Products is the arm that markets drugs, infant formula and adult nutritional products.
The effect of walnut intake on factors related to prostate and vascular health in older men. Funded by the California Walnut Commission, who also funded at least two other papers that I can find, including
An increase in dietary n-3 fatty acids decreases a marker of bone resorption in humans.
This doesn't necessarily mean that the results are invalid. Researchers, unfortunately, all too often have to find funding from sources who are not uninterested in the outcome.
Jeff will be able to tell you about that particular study. I wouldn't be surprised to see the California Walnut Commission again, though!