If that goes too far, do something like the UK's Data Protection Act of 1998 that insists almost all PII is subject to review by the individual and they can demand erroneous data be fixed. They can also demand deletion in various scenarios.
But personally, I like the copyright idea. If a copy of a song can be protected from being made legally, even if I personally make the copy, I see no reason why my most personal of details cannot be similarly protected.