"Polyphenols" are just one type of antioxidant. Does this study cover vitamins which can also be antioxidant? If not, and they're only comparing that one type of antioxidant here, it's likely that fresh fruits and vegetables have much more antioxidants per serving (just not that specific type).
Based on that article, they studied just polyphenols. Unfortunately, I could not find the actual study online. I don't think that anyone should start replacing fresh fruits and vegetables with popcorn in large amounts based on this article. What I take from it is that popcorn can be healthy and tasty snack that comes with significant amount of polyphenols (from the Science Daily article):
Previous studies found low concentrations of free polyphenols in popcorn, but Vinson's team did the first study to calculate total polyphenols in popcorn. The amounts of these antioxidants were much higher than previously believed, he said. The levels of polyphenols rivaled those in nuts and were up to 15 times greater than whole-grain tortilla chips.
This was also interesting:
In another surprising finding, the researchers discovered that the hulls of the popcorn -- the part that everyone hates for its tendency to get caught in the teeth -- actually has the highest concentration of polyphenols and fiber.
"Those hulls deserve more respect," said Vinson, who is with the University of Scranton in Pennsylvania. "They are nutritional gold nuggets."
I have been wondering the same thing about hemp seeds. Many prefer the shelled version, but I tend to eat the seeds with hulls. It seems to be obvious that with the hull comes more fiber, but the antioxidant content is still quite unclear.