Yes, but you are designing a system based on a once in 100,000 edge case. There is no reason why such odd and rare requests can't be handled in a customer support request.
...If your customer service team are sufficiently well staffed, trained and have escalation points. In the article the customer service team couldn't even read a decision made by 'The Back End Team'.
A more realistic case for you: People make far more mistakes than you think. Having done genealogy recently, the number of documents with people messing up their own birthdate or name is staggering. On top of the much larger number of registers where someone else have taken the information down wrong.
You're seriously underestimating gow much this happens with current rates of immigration. 1 in 1000 to 1 in 5000 seems to be the correct rate in my country.
Besides, Even with 1 in 100k, with the US population of 330 million, you've created trouble for 3 300 people based on this edge case alone.