You're either missing the point again, or intentionally asking at what point you can stop acknowledging prior contributions to claim it as your own. Let's change it from food.

"At what point can I claim I invented math after it was taught to me?" - as long as it was taught and you didn't discover it completely on your own, never. The work was built on the work of those that came before.

"At what point can I claim I invented computer technology without any assistance from any societies, technologies, or ideas from previous people or previous civilizations?" - If at birth you were left on a deserted island, and by yourself survived, created all tech by yourself, then yes. Otherwise, never.

So while you can say "Apple pie is part of American culture" and be correct, it will also always be true that American culture got parts of its culture from other cultures.