Love the typo - we should all be non-naive teachers ...
Seriously .... I work as a teacher trainer with both native and non-native speaker teachers, and I don't think that there's a simple answer. First of all, I'd want to know : is the person (whether NS or NNS) a good teacher? I honestly think that's the most important thing. Secondly, does s/he have a sufficiently accurate language competence (which may involve cultural knowledge) to teach the level and type of students involved.
For instance, if I had a young child learning English for the first time, I'd be far more interested in the teacher's ability to make the lessons fun and to motivate kids than their knowledge of phrasal verbs. If I were looking for a teacher for an advanced level somewhat agressive managing director of a multinational, I'd apply different criteria - but again, might decide that a teacher with close to native proficiency, a confident personality and a lot of business experience was preferable to the other teacher I had available who, though native speaker, was young and inexperienced, had never worked or taught in a company environment, was very shy and unconfident etc.
As far as how close a non-native speaker can get to native speaker competence - I have known a few teachers who were completely indistinguishable from native speakers, and several more whose spoken English was indistinguishable even though their academic essays showed a certain amount of inaccuracy. Again, I might not put these teachers on very high-level courses which involved writing skills, but they would have been fine on at least 70% of course types. But quite honestly, I've known a lot more native speaker teachers of whom I'd say the same.
You also have to take into consideration the fact that native-speaker English is no longer a necessary model for a large number of learners. My students, for example, are constantly involved in international meetings - with Germans, Latvians, French, Spanish, Hungarian, Swedish ... and every other European nationality. The British and Irish make an occasional appearance, but if present at all are always a minority. English is spoken as a lingua franca, and in an international version that wipes out the idioms, phrasal verbs, reduction in pronunciation etc etc that are the main stumbling blocks for non-native speakers. I've known quite a lot of non-native speakers who could, therefore, do my job as well as me from the linguistic point of view.
I think you always have to evaluate the person as an individual, and in relation to the situation. There is currently, (at least in Europe, and in my opinion very unfair) market-driven prejudice against non-native speakers that refuses to take these factors into account. I am NOT saying that you accept anyone who walks in - linguistic competence must always be evaluated. But don't rule out NNSs out of hand.