As always, the answer is: "it's a machlokes!"
Open up a Shulchan Aruch to Yoreh Deah 116:2, where it says not to mix meat and fish.
The Taz's opinion is that because meat-and-fish is a health concern, we are stricter about it than normal kashrus prohibitions, therefore if you pour one ounce of fish juice into a hundred ounces of beef broth, you may not eat it.
The Nekudos HaKesef (written by his buddy, the Shach, and his son) argues. If the Talmud never gave any different guidance (as it does for all sorts of things that "aren't even batel in a thousand"), we default to the batel-by-60 policy. Okay, actual venom is not batel, but it never said anywhere that fish-with-meat is quite that dangerous!
Broadly speaking, we tend to follow the Shach (& co.) over the Taz in situations like this. And that's the OU's position.
Next time you go to the supermarket, take a careful look: the name-brand Worcestershire sauce is marked OU-Fish, while the generic brand is not. Both contain anchovies. The former has more than 1.6% anchovies by volume (i.e. is not batel), the latter does not.
Some Chasidim, however, follow the Taz's opinion. Tropicana makes (or at least made?) an orange juice with "extra Omega-3" derived from fish oil. It's marked OK-Fish. The OK put out a statement that the fish content is nowhere near 1.6% by volume so it's totally batel; however, the Fish warning is for those who follow the Taz's stringency that fish is not batel.