Dr. Guyenet has a good post on a similar paper:
http://wholehealthsource.blogspot.co...n-at-door.html
My personal thought is that PUFAs HAVE been part of our evolutionary history, mostly in the form of fishy things, and I think it's more important to ask yourself, could a peasant with limited technology make this? before you eat something, rather than quibble about the specific omega 3:6 ratio or biochemical makeup. So, sunflower seed oil? Sure, you can make that reasonably easily - I saw a do-it-yourself plan using a hydraulic jack, but a screw mechanism, even a wooden one, would work fine. Indian people have been using canola oil (the traditional type, mustard seed oil, not industrial stuff) and Chinese people have used sesame oil extracted using the same process for centuries. Granted, these were more for flavour than as a cooking medium, but they've been around, I don't think you have to avoid them entirely.
As for the study... meh. There are so many games you can play with data and statistics, with the number of factors they were looking at and the relative unreliability of self-reports AND the difficulty inherent in extrapolating the actual balance of polyunsaturates, monounsaturates & saturates from food that the researchers never even saw, never mind questioned sources (we know that all meat products, including eggs, have different fat composition depending on their sources)... the results may be "statistically significant" but they are still small, and don't, in my mind, warrant deviating from a time-tested type of diet.