It was the result of a complaint of somebody who had assumed an act of prostitution was taking place.
An officer can affect an arrest, if there is cause. He had reason to ask for her identity and she refused, so that is why she was arrested.
It was justifiable.
Would the complaint based on a man and a woman kissing have been made if they were both white? Would the officer have pursued a complaint based on a man and a woman kissing if they were both white? I doubt it.
States can require you to STATE your name to the police (Hiibel v. Sixth Judicial District Court of Nevada) but not to produce ID. Not all states have this requirement though. California's law requiring people to produce ID on demand was struck down in Kolender v. Lawson.
Even stating your name is required ONLY if the police have a reasonable belief that the you are involved in criminal activity.
Going only by her side of the story it doesn't seem that the cops had much to go on.