Jarrett is in her 60s. She left Iran at age 5, early in JFK's Presidency. The current regime started in 1979, over 15 years later.
I don't have any love for Jarrett, but the anachronisms are rather great. Her parents are both US-born Americans, both African-American (i.e. not of Persian/Iranian heritage). And the evidence that Jarrett is Iranian is, well, non-existent. The whole thing is a CT, and a pretty low-grade one.
BTW, my Dad and his brothers were the US-born sons of German-speaking parents. The one who was not 4-F served in the US Army during WW2, against the Nazis.