They are saying the opposite. People have been coming to America for higher education and staying here and that has historically benefited the US. And that seems to be changing.
I would say there was a brain drain from Iran to the US but I've also heard it used as a transitive verb. I think if there is a clear place talent is moving it's useful to specify it (and fwiw it doesn't sound weird to my ear).
However that's not what brain drain means. You would say "Iran had a brain drain in the 70s" not "America was brain draining Iran" makes no sense.