Police can't figure out your parent's fingerprint from looking at your fingerprint. Only 4 states collect fingerprints from driver's licenses; California does so only to do a background check for certain kinds of vehicle industry occupational licensing.

Also applying for a license means you are at or approaching the age of majority. Either you are applying for a license knowing that you once did a crime, or you're doing a crime knowing you once submitted a fingerprint for a license. That's very different from having your blood sampled as a newborn, and most people assume their health information had privacy protection.

Apples and oranges are both fruits, but they're not interchangeable.