The author means by this quote that immigrants once naturalized should be able to serve as the president of the United States. I agree to a degree with the authors statement. When the author brings up Hamilton as an example of someone who migrated and was allowed to run for president he leaves out that in this case Hamilton was still just a young adult when he came to the then colonies. Hamilton also fought during the revolutionary war helping to develop the foundation of the United States which would make there be little to no reason in his case to doubt his loyalties. However in the case of recent immigrants or ones who have migrated after living a majority of their life (Say a 50 year old) in a foreign country it would be hard to really tell where their loyalties lie. I am not saying that every immigrant who would want to run for leader of the United States would have bad intentions, but that they may subliminally favor there home country in foreign affairs.
For example lets say that a 50 year old Swedish man/ woman immigrates here, and eventually gains citizenship. They have a previous political background in their home country and good finances so it is not hard for them to fall into American politics. By the time they are 65, lets say, they decide to run for president and win. If they have to complete a trade deal with Sweden they may be more inclined to accept a deal that favors them, or to not hold them accountable for transgressions that may deserve sanctions.
In finally I do agree with the authors point that migrants who do come here say as children or at an age where they can still spend a majority of their life in the United States before running fro president should be allowed to. However there should still be certain restrictions to prevent electing an unfit leader.