The things being measured are different. To a first approximation, all native speakers do maximally well at sounding like a native speaker.

Lumifer's friend may indeed speak like a native speaker (though it's rare for people who learned as adults to do so), but she cannot be better at it than "most 'natives'".

What she can be better at than most natives is:

• Vocabulary.
• Speaking a high-status dialect (e.g., avoiding third person singular "don't", double negatives, and "there's" + plural).
• Using complex sentence structures.
• Avoiding disfluencies.

It is possible, though, for a lower-status dialect to be more complex than a higher-status one. Example: the Black English verb system.