Without question, you are spot on and I should have explicitly stated mercury testing, yet most independent third party labs, if not all, test for mercury when testing fish oil among other things.
Also, a lot of fish oil out there is molecularly distilled and after that process is at or near pharmaceutical grade levels. The Carlson fish oil that I take is tested in accordance with AOAC international protocols by an FDA-registered lab to ensure freshness, potency, and free of detrimental levels of mercury, cadmium, PCB's and 28 other contaminants.
Besides Carlson, the other brands I like are Dr. Sears Zone Omega Rx, which has the highest EPA and DHA, though, it's very expensive and doesn't taste great and Ascenta NurtraSea, which is very similar to Carlson, but more expensive.
In fact, I wouldn't buy a fish oil that wasn't third party tested. Plus the ones I mentioned use small cold water fatty fish such as sardines, anchovies, mackerel, and herring, but larger fish from the ocean or fish farms are more likely to contain toxin levels of mercury or pesticides. I am more concerned and limit eating sushi, fresh water fish and long living large ocean fish such as, but not limited to salmon, tuna, swordfish, and sharks because of the high mercury content and other contaminants.