So the implication is that the director is the one who has raped Reagan and thus invoking this demonic presence into her.

One of the things that has to be understood is that the time period Alex is discussing when blood product from people with HIV was being used to make Factor VIII was when Reagan was in office. He was president through pretty much the entire 1980s, which is when the AIDS crisis was at its most tragic. And one of the things that made it worse was that Reagan was someone who was staunchly opposed to any governmental regulation, including ones related to public health. So he was resistant to putting things in place that would have helped. mitigate the damage that was being done.