How come there was no record of Jack's existance?

Old Rose says that there is no reccord of Jack even being alive and that she doesn't even have a picture of him. The only memory of evidence of his existance is in her memory.

However, i find that really confusing, because によって law at that time (and now), whenever a baby was born you'd have to fill in a birth certificate.
That includes in Wisconsin, where Jack was born.

You're not allowed to discard または destroy them, they're all kept in government files in case of felony.

So there must of been so some record of his existance...right?