What I really disagree with is your logic and your conclusion. The constitution lays out the qualifications. It doesn't address computers, each county's records, etc. Therefore the method of verification of these qualifications changes over time and with advancing technology and legal requirements.
If OB or anyone else doesn't meet the qualifications they should be out. Even if it is discovered when they are in office. If you're not qualified, you're out, whenever.
So let's air the proof and move on (not . org).
Often, in colonial times, the records were kept by churches. There would be a record of christening that substituted for birth records. County governments absorbed those records over the years as they took over more record-keeping functions. The Constitution helped codify the need for reliable and comprehensive records by requiring a decennial census.
If OB or anyone else doesn't meet the qualifications they should be out. Even if it is discovered when they are in office. If you're not qualified, you're out, whenever.
The question is who makes that determination. There is no precedent for the federal judiciary to declare a candidate ineligible to run for the office, and it is the states that determine who appears on the ballot and how the electors may vote. Even if the federal courts were to weigh in on the issue, it is not clear who has the burden of proof or who has standing to bring the suit, and the courts are likely to err on the side of inaction.
The Constitution and two centuries of precedent are pretty clear that the courts cannot remove a federal elected official from office. The president, vice president and federal judges must be removed by impeachment, members of Congress expelled by the House or Senate. The proof would have to be overwhelming to remove a sitting president.