Q : What prevents any alien from claiming this status by saying they were a victim of a crime?

A petition for U nonimmigrant status must also contain a certification of helpfulness from a "certifying agency." That means the victim must provide a U Nonimmigrant Status Certification (Form I-918, Supplement B) from a federal, state, or local law enforcement agency that demonstrates the petitioner "has been helpful, is being helpful, or is likely to be helpful" in the investigation or prosecution of the criminal activity. Further the head of the agency must sign the certification.