She didn't have to talk, she had the right to remain silent. They went on to tell her she had the right to remain silent yet arrested her for it. When she was at the station their boss apologized and said that the troopers were mistaken.
How is it antagonizing to simply refuse to speak? You have a right to be silent.
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No, it's more like the officers didn't know she had the right to remain silent and arrested her for exercising her right to remain silent. Once at the station they apologized and their boss said they were mistaken. The officers didn't know the law.