In response to the title question, my response would be to make sure you don't consume so many dietary PUFAs that you have arachidonic acid (or EPA or another long-chain omega 3 PUFA).  There is no way to know exactly how many milligrams of dietary omega 6 PUFAs, for example, you can consume in order not to have AA in your cells - it will vary from one person to another.  The omega 3/6 balance thing is a pure fiction, based upon the observation that AA metabolization is inhibited (at least to some degree and temporarily) by things like fish oil.  However, this does not mean that an omega 3 rich diet is safe, and it appears to be less safe than an omega 6 rich diet.  Did you read the page on fish oil quotes?  If not, take a look at that information.

 

Any unsaturated fatty acid can get oxidized, no matter what form of fat it is in, but if it does, and your body is in good health, and there are not a lot of other unsaturated fatty acids getting "attacked" by radicals, then it won't cause any problems.  You might be able to eat an omega 6 PUFA (linoleic acid) rich diet and still be healthy, but you would need to eat a lot of antioxidant-rich food.  There is no way to know for sure what would happen, because it is a long-term health issue.  You might eat the wrong antioxidants or not enough by a small margin, and then find yourself with this or that "disease."  Then there are oils that, if fresh, may be okay, such as sesame oil, even though it is rich in omega 6 PUFAs.  However, I'm not willing to take the chance with my health.  A tiny amount of fresh, organic tahini, for example, is not likely to cause problems if you do everything else healthy, but supplementing with fish oil makes no sense at all to me, because there are better ways of dealing with AA metabolites, and I suggest getting the AA out of your cells anyway, though it takes about 2 years.