Lying is not necessarily fraud. Nor would it be fraud in this case. Lying to the police can be a crime, in most jurisdictions this is called Obstruction of Justice. But the girl was not charged with that.
What baffles me the most about this case was the rigamarole everyone went through to determine that she had a phone. Why did it matter? If the teacher saw the phone, that's the end of it. Give the pupil the appropriate punishment. (detention, suspension, saturday school, etc) Why did it have to be proved beyond a shadow of a doubt that she did in fact possess a phone? What if she had passed the phone off to a friend before the officer arrived? Would they have then had to let her go unpunished? The incident originally wasn't about her committing a legal crime, it was about breaking school rules. When you're talking about breaking school rules you don't need evidence beyond a reasonable doubt to get a "conviction".