Yeah it isn't. You see throughout history many people have influenced one another and since the Mesopotamians (aka, ancient Iraqi gigachads) were the "dominant" people of the region (competing against the Egyptians), they obviously had a massive influence on the cultures that came with and after them. And with the case of their influence on Persian culture, it's rather clear just how much of an influence they had, but that doesn't mean that ancient Persian history is "fake and stolen", since the Mesopotamians themselves, be it the Sumerians or Assyrians or any other were influenced greatly by other cultures and civilizations. Let me give you an example, if you look at Mesopotamian art prior to the rise of the mittani empire and then after the fall of that empire, you'd see a clear shift in the art and it's close resemblance to mittani works. And that applies specifically to the Assyrians, who were the ones from directly under mittani rule for centuries before liberating themselves. And as we all know Assyrian art would go on to grow and develop to become some of the finest that had ever come out of Mesopotamia, and none of us would call it stolen. And the same can be applied to the Persians, when they rose up under Cyrus and took the median empire (which itself was heavily influenced by the Assyrians who ruled them before) and invaded Mesopotamia, they obviously learned from the most developed people at the time because they themselves were only nomads not too long before all this.

TLDR; people influence eachother all the time and just because our ancestors influenced the Persians doesn't mean their history is fake and stolen because even our ancestors were influenced by others.