Friends of mine who moved to the US as teens have what I would call off-native. Their mastery is definitely native-level but their accent is a bit odd. You might wonder if their accent is just an American one you haven't heard before. A good example of this level of English proficiency is YongYea on YouTube.
One detail the article does not discuss is the distinction between oral and written competence.
I started learning English in my teens. I would judge my reading and writing proficiency to be at the higher end of the native speaker spectrum. I speak fluently as well, but have retained a distinctly non-native accent, and I sometimes have difficulties understanding spoken English (getting older does not help there either…).