Because Zoroastrian Parsi were the original Persians before Islamisation of Iran and therefore closer to the ancietn Persians and closer to the source.
Iran was invaded by the Turco-Mongols and Arabs, but Parsi were still the unmixed original Persians who survived Islamisation. And those Parsi were even much more natives of the Iranian Plateau than current Persians. Those Parsi had much more Neo_Iran Plateau auDNA and there was no Steppes ancestry in them.
Iranian Plateau is HUGE. Elamites lived only in a small part next to the Persian Gulf. Sure, it is possible that Elamites were later Persianized by the Persians in Elam, but that doesn’t rule out at all that Iranic people came from the NorthWestern parts of the Iranian Plateau.
Ancient Turkmenistan = BMAC. And today we know the genetic profile of the BMAC. It was mostly Iranic. And has NOTHING to do with the Andronovo.
https://i.postimg.cc/C1c4hB63/map-elamite.jpg