The US Food and Drug Administration suggests we all get up to 3 grams of Omega-3 oil daily.
This equates to 10 1-gram fish oil concentrate pills (only 300 mg of each are Omega-3's).
The report, dated September 2004, suggested that more than that amount could reduce clotting and have the other effects of which you and I are speaking.
Since a serving of salmon has 1 gram of Omega-3's, one would need three servings a day of salmon (the most Omega-3 dense fish) to meet the point at which the caution occurs.
Therefore, going beyond that amount is where the risk comes in.
I don't know anyone who would be going much beyond three helpings of salmon each and every day, do you?
http://www.fda.gov/bbs/topics/news/2004/NEW01115.html