Debate over children who do not grow up speaking English as a 1st language

I had a talk yesterday with a friend who told me that if children in America do not grow up with English as their first language, they will always lag behind in school. She is from Mexico and seemingly quite successful so I don't understand her logic. I know that the kids in the classroom where I volunteer are struggling. Still, I believe that they can not only learn but excel and that it is now a challenge for me. I think that her perspective if flawed and that we will need to have further discussions on the subject.