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 por 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 o 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?