The federal law and the law of most states only requires the permission of one of the participants to record a conversation. There are twelve states that require the permission of both (or all) parties. Obviously, Washington, DC, is not a state and so it's not a two-party consent jurisdiction.
But this isn't a case of two people meeting at Starbucks for a blind date. This is the White House, the headquarters of the President of the United States. I would think there are some internal rules and regulations that govern what can be recorded, and by whom. What has me seriously concerned is just how the [bleep] she was able to make all these recordings without the Secret Service being aware of it. Aren't they supposed to on top of illicit bugs in the White House?