But the US has moved much more towards "no smoke without fire", leaving the release of names in an antiquated place.
Bogus charges get dropped all the time, but the mugshot and uncharged arresting reason are still posted for all.
This is a dangerous tool in the hands of a flawed institution. We know that people get arrested for trumped up charges, or outright fabrications that later get silently dropped.
Point being, if all you do is maintain a list of names of who you have in custody, you are fulfilling the American Habeas Corpus requirements. There's no constitutional requirement that mugshots need to be released publicly on the internet, there's no rule that the police need to announce what crime a person is suspected of before a charge has been laid. Americans can maintain a healthy distrust of police without wholesale public release on the internet of the details of an arrest.