Todd, the paper to which you refer was published with a half dozen companion papers which all seem to reach slightly different conclusions. It's not clear to me that we can disregard dietary AA. (These links should open in a second window.)

The effect of dietary arachidonic acid on plasma lipoprotein distributions, apoproteins, blood lipid levels, and tissue fatty acid composition in humans
After consuming the high-AA diet, the total red blood cell fatty acid composition was significantly enriched in AA which mainly replaced linoleic acid. These results indicate that dietary AA is incorporated into tissue lipids, but selectively into different tissues and lipid classes. Perhaps more importantly, the results demonstrate that dietary AA does not alter blood lipids or lipoprotein levels or have obvious adverse health effects at this level and duration of feeding.

The effect of dietary arachidonic acid on platelet function, platelet fatty acid composition, and blood coagulation in humans
The results from this study on blood clotting parameters and in vitro platelet aggregation suggest that adding 1.5 g/d of dietary AA for 50 d to a typical Western diet containing about 200 mg of AA produces no observable physiological changes in blood coagulation and thrombotic tendencies in healthy, adult males compared to the unsupplemented diet. Thus, moderate intakes of foods high in AA have few effects on blood coagulation, platelet function, or platelet fatty acid composition.

Increased dietary arachidonic acid enhances the synthesis of vasoactive eicosanoids in humans
Thus both the metabolites of thromboxane and PGI2 increase on the high-AA diet. Furthermore, both indicated changes in metabolite excretion may be associated with measurable effects on several physiologically significant cellular functions, such as platelet aggregation in vivo and inflammation in response to immune challenges.

Same authors - same study - same issue of same journal - what the heck is going on?