I'm not confident that many copy editors in publishing houses or on newspapers/magazines – British ones, at least – have a particularly conscious knowledge of grammar, unless they happen to specialise in linguistics; if they do have a reference work on their desk, it tends to be Partridge or Fowler, or the Times Style Guide. So perhaps in such cases we're simply exchanging the writer's native speaker's intuition for his editor's!
To answer my own question: perhaps native speaker intuition is "unreliable" where someone insists that a non-standard usage (e.g. "between you and I") is standard. But I'm not sure whether that's what Milky meant.
MrP