She was not arrested for yelling a racial name at the cop. She was arrested for disorderly conduct. Disorderly conduct laws are on the books to allow the police to arrest anyone they want. When no being abused that is probably ok as it allows the police to defuses situations before a serious life changing crime is committed in anger.
http://antiprotester.blogspot.com/2006/09/duke-lacrosse-rape-case-is-tawana.html
Duke Lacrosse Rape Case Is Tawana Brawley Redux
http://leadandgold.blogspot.com/archives/2006_09_01_leadandgold_archive.html#115921935524818146
Duke lacrosse: Custom, interest, and the pursuit of truth