I agree with your comment. However, I am puzzled by the SS action here. He was investigating a threat/possible threat/instigation of violence against POTUS. That is his job. I am pretty certain he has the legal tools at his disposal to take this woman in for questioning. So I am wondering what he intended to accomplish in the first place.
I agree that she should be questioned for such a thing but where she did not make a direct and specific threat that SHE was going to do anything then she didn’t commit a crime.
The correct action was to let her know she attracted attention and I’d say she got the message.
The only legal tool to do that, barring her voluntary submittal, is to arrest her. There is no “right” to question anybody, even somebody under arrest. Maybe, especially somebody under arrest.