Curious if you read the article? The point that it is making is that immigration didn't write down people's names at all, they were just checking them off a list, so there was no opportunity to alter, change, or butcher the names. It surely happened, but either before or after; don't blame the immigration official.

In reality, immigration officials did not write names down—they checked them off on a list in front of them. In other words, the names were already written down. The officials were not working with blank sheets of paper on which they created lists of newly arrived passengers, but with ship manifests, official lists of passengers who had disembarked. These manifests were required by US federal law as of March 2, 1819. Beginning on that date (i.e., when the federal government assumed control over immigration), ship captains were required to report a list of all passengers brought to US shores from foreign countries; information required included name, sex, age, and occupation