There was nothing in the piece that said that. Her point is that we NEED immigrants,
Go to the third paragraph from the bottom and you will find the open borders arguments you refuse to see, namely that economically strong nations have an obligation to accomodate immigration flows.
Overall, this author is conceding a lot of ground to immigration critics about the breakdown of assimilation in the United States and the impact of mass immigration, but only speaks in generalities about how to fix it and she insists that the flow keep coming in. That attitude is what makes the bolded comment accurate.
You can call that 'open borders' if you like, I don't choose to.