It is the responsibility of the school or university to be certain that they are hiring a quality native speaker.

@Rebecca:

I am not a native English speaker either, but my accent is clearly British with a slight Cockney touch. I have published books in English and lectured in English for a long time, also at unis and colleges in the USA. In China, I have seen so-called native speakers who can't count till ten and write its when it should be it's. There are other things I could mention regarding the deficits they have in using their own language, and I am wondering how they could be "teachers" at all when looking at their poor educational profile.
So, being a native speaker is no guarantee whatsoever that students will get the best education they deserve; it depends much more on the individual person and the school to appoint a duly qualified teacher - a thing that rarely happens in China!

@Sanjeevi:

Your name sounds Indian, and especially Indians have such a strong accent that you hardly can understand them at times although otherwise their written level of English may be excellent or even near-native.

The problem is the crappy EFL labour market that demands low-educational profiles and not too well qualified teachers to keep expenses in employing at a minimum level. That crappy industry gets what it deserves.

And yes, I am berffekt in Chinglish....LOL