I've personally been involved in situations where a student's refusal to cooperate lead to the situation escalating far beyond what was necessary. I think sometimes they believe that if they dig in their heels, nothing bad will happen and the adult will let up. They don't understand that digging in just escalates the situation. When I encounter such a student, I usually have to explain the complete consequences of their actions (including ultimately getting cuffed and hauled out if need be), before they relent.
From reading the report, it's pretty clear that the student had multiple opportunities to come clean before being arrested, and refused to take advantage of them. Yes, I agree that arresting the girl was overkill, but the report mentions that the officer had prior [negative] dealings with the student before, so I would suspect that there is a story here that goes back a little farther than "ZOMG STUDENT ARRESTED FOR TEXTING." Arresting the girl was overkill *if* this was her first disciplinary issue. If this is one of a long string of issues, it's a different story. When sane, measured discipline isn't getting through to a kid, it may be a good time to over-react and try to get the kid's attention.
I don't know the kid, and I don't know her history, so I can't judge whether or not the officer was out of line. I can imagine plenty of scenarios where it is, and plenty where it isn't. I've had students get in a disproportionate amount of trouble for similarly stupid reasons, and it usually plays out the same way: a student with a long disciplinary history tries to press their luck over something moronic, and comes up with the short straw.