Visa has to respect whatever laws apply in the country they operate in. So if the police want Visa info on whoever, provided that a legal framework cover this issue, Visa has to give it. It makes 0 difference if the payment system is government-operated or not. In any democratic country, the police would need the approval of a judge whether the service is public or a private company. And in dictatorship, the government will get the data or ban you from doing business in the country anyway.