Privacy laws don’t prevent you from divulging your private information to anyone you choose. The laws prevent third parties from sharing your information without your permission.
For example, if Rocker willingly agrees to hand over his medical records, he may do so. But if he doesn’t want to, Ms. OneNightStand can not compell him to even if his name was on the birth certificate.
It’s also not likely that anyone would actually go through the effort of collecting all of their medial records, or even know how to go about it. Plus, a whack of those records are probably not relevant to offspring as far as any need-to-know scenario. Eg/ If rocker got his junk surgically enhanced so he looked extra-manly onstage in his tight rocker pants, his kid doesn’t need to know it. It doesn’t affect the kid, it’s no one else’s business, and Rocker may wish that to be kept quiet.
If Ms. OneNight asks nicely, it’s Rocker’s prerogative to divulge any hereditary conditions he may know about in his family history.