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They mean that Flying Blade only works with finishers that specifically mention Precise Strike in their text.Precise Strike
... If the strike is part of a finisher, the additional damage is 2d6 precision damage instead...
All Finishers "can benefit from your precise strike," but not all Finishers require precise strike.
The difference is that the Finisher Trait does not require Agile or Finesse weapons. Some specific finishers, however, do require (e.g. Confident Finisher: "Make a Strike with a weapon or unarmed attack that would apply your precise strike damage") Agile or Finesse weapons.
Therefore, Dual Finisher, even without any language in the feat specifically mentioning Precise Strike, meets the "any other finisher that includes a Strike that can benefit from your precise strike" qualifier for Flying Blades.