Re-read my link,a car that has a missing or damaged vin tag can be issued a new tag with the smae number by the state and attached to the factory dash location-not a state issued vin number on a door sticker.
Can be? Sure.
But really read what it says, note the word "if" is used repeatedly, also note the word "or". In some cases, original VINs are not available from the manufacturer. Quote below is from your link;
(A) If the registrar determines that the applicant has complied fully with the requirements of rule 4501:1-11-01 of the Administrative Code, a replacement VIN plate or replacement vehicle parts derivative VIN plates, die impressions, or stickers shall be obtained and installed in accordance with this rule.
(B) If it is practical to do so, the registrar shall authorize the use of the original VIN. If it is not practical to authorize the use of the original VIN, the registrar shall assign a new VIN to be used for all purposes in identifying the vehicle and its parts.
(C) If the registrar determines that a duplicate original VIN plate is reasonably available from the original manufacturer of the vehicle, the registrar shall obtain a duplicate original VIN plate to be installed in accordance with this rule.
(D) If the registrar determines that a duplicate original VIN plate is not reasonably available from the original manufacturer of the vehicle, the registrar shall cause an “Ohio replacement VIN” plate to be produced. Said Ohio replacement VIN plate may be produced by the bureau of motor vehicles, the highway patrol, or any other source as prescribed by the registrar. The registrar shall prescribe the size and design of the Ohio replacement VIN plate, which shall be designed to restore the identification of the vehicle in a manner that will deter its theft and facilitate its marketability to the extent that is practical to do so. If it is practical to do so the Ohio replacement VIN plate shall be designed for installation in the manufacturer’s original location. The Ohio replacement VIN plate shall contain such security features as the registrar may prescribe.