I think a more realistic threat is hemorrhagic stroke. You'll see some of the highest rates of stroke in people who consume the most omega-3s, such as the Japanese. I can't say whether that is causative, but I think it's likely. n-6 fats are maligned everywhere these days, but they're essential and their clotting nature should balance out the hemorrhaging nature of n-3 in the diet.

Here's one paper I've seen (free full text):

Dietary supplementation with eicosapentaenoic acid, but not with other long-chain n-3 or n-6 polyunsaturated fatty acids, decreases natural killer cell activity in healthy subjects aged >55 y

Edit- here's another:

Dose-related effects of eicosapentaenoic acid on innate immune function in healthy humans: a comparison of young and older men

I agree that EPA antagonizes the immune response. We need it in small amounts but in larger amounts it becomes detrimental. In fish and brains it is only a very minor part of the fat, with DHA being more abundant. However in fish oil you have a weird ethyl ester of more EPA than DHA. Best to just eat fish and brains and fish brains and brainy fish if those exist. And not as much as the Inuit.

There is going to be an optimal range of EPA intake, too little makes the risk for depression skyrocket, too much and you can get keeled by bacteria.

Omega-3 fats may no be so great if you catch Influenza and you are a mouse.

Fish Oil-Fed Mice Have Impaired Resistance to Influenza Infection

Although fish oil-fed mice had lower lung inflammation compared with controls, fish oil feeding also resulted in a 40% higher mortality rate, a 70% higher lung viral load at d 7 post infection, and a prolonged recovery period following infection.

(The control mice were fed corn oil)

Fish Oil Feeding Delays Influenza Virus Clearance and Impairs Production of Interferon-γ...

The present study demonstrates a delay in virus clearance in mice fed fish oil associated with reduced IFN-γ and antibody production and a greater weight loss and suppression of appetite following influenza virus infection.

Fish oil feeding enhances lymphocyte proliferation but impairs virus-specific T lymphocyte cytotoxicity...

The results showed that, despite improved lymphocyte proliferation, fish oil impairs primary virus-specific T lymphocyte cytotoxicity. This impairment may explain the delayed virus clearance that we have previously reported in infected mice fed the fish oil diet.

You need omega-3 and 6 in the proper balance. The main reason we pay so much attention to getting more omega-3 is that our diets tend to be so high in omega-6 (thanks to the ubiquity of cheap soy bean oil in absolutely everything). We do need omega-6's though. Both are considered to be essential fatty acids. So, yeah, getting too much omega-3 could potentially be a problem too. These two EFA's balance each other out so that the body's inflammatory response is appropriate to deal with whatever infection or injury that we might have to deal with. If you have too much omega-3 then it's going to overpower what might be an appropriate response to infection or injury. There is also the added risk of bleeding when you consume too much.

Omega 3 will oxidize. Over consuming Omega 3 makes this worse. I work to reduce omega 6 so I can consume as little omega 3 as possible and still have a decent ratio.