This is a link to the actual study. Page 16 is relevant.
http://oceana.org/sites/default/files/reports/National_Seafo...
The group tested 114 tuna samples. Of those 114, 66 were of a fish that the vendor was calling "White Tuna". Have you ever eaten something called White Tuna? Neither have I. It's a fairly unpopular sushi fish sold sparsely around the country.
Why does it make up more half the sample, you might ask? Well, it turns out there is essentially no such thing as White Tuna. Hence 94% of the samples are "mislabeled." [the authors assert that a certain type of albacore tuna sold in a certain form counts as 'white tuna', which accounts for the 6% of correct labels] If your goal was to achieve a result which shows lots of mislabeling, a good strategy would be to considerably oversample 'white tuna'.
They took 48 more samples of tuna other than 'white tuna'. Notably, that didn't include anything from a can, which is by a WIDE margin what most americans think of when they think of tuna. Nevertheless, of those 48, they determined that five were "mislabeled" due to the tuna actually being a substituted variety of tuna. In other words, all 48 were 'tuna', though perhaps not 'albacore' or the specific type it claimed to be.
So where does that leave us? More than half of the samples were of a fish known to be commonly "mislabeled" by standard industry practice, and the rest of the mislabelings were substitutions of one type of tuna for another. In no universe does that lead to the conclusion that 59% of the tuna Americans consume is not actually "tuna". I would venture that no one reading this comment has ever eaten a piece of tuna that was not actually from a tuna fish (though _maybe_ they lied about which specific variety you were eating).
This organization has a history of running biased studies and then churning out ridiculous charts and headlines to push on local newspapers. They ran with a version of this story in New York City around a year ago. It's nonsense. Eat your tuna and enjoy it.