I believe you have confused "public record" with "public domain". Public domain means that there is no copyright for a work, so anyone at all is free to use it for any purpose. The public record, on the other hand, consists of documents which are made accessible to the public by the government in accordance with law, which allows people to view the documents, but not necessarily any more than that.
There is a lot of overlap between the two, because the public record naturally consists of many government-produced documents, which are often automatically in the public domain by law. A mugshot taken by a federal officer, for example, is typically a public record in the public domain. But there may be documents in the public record which are not in the public domain - for example, the plans for a proposed new City Hall will be in the public record, but the copyright may still be owned by the architect. And of course, there are many works that don't concern the government at all which are in the public domain but not the public record.
Generally, non-governmental copyrighted materials do not automatically lose their copyrighted status and enter the public domain by becoming part of the public record. Some portions of the Epstein files such as reports created by federal workers in the course of their investigation would likely be public domain public records. Other portions, like photographs and emails created by individuals and later collected as evidence, would not have their copyright status changed by entering the public record as evidence in a police case. Whether a particular photo is public domain or just in the public record will in general come down to who originally took the photo, which is what ultimately determines who owns the intellectual property.