The bottom line in my opinion is that Chinese students would be better served by those who have had at least a modicum of training in ESL/EFL. However, I do believe there are native speakers who have either the academic qualifications and/or the innate ability to take on English classes in China or any other foreign countries. Apparently this is the position of the Chinese government as well. That is, they feel the importance of English instruction requires that serious consideration be given those with degrees in any discipline and/or documented "qualifications" of some kind.
It's that gray area of "qualifications" that is troublesome. It leaves too many loop holes through which those with no desire to be real teachers can find their way into the classroom as a means of fulfilling alternative agendas.
However, I'm currently teaching alongside and coordinating teachers who are either still working on their first degree or have degrees in other disciplines. The FAO of the university and the College director feel as though they have the necessary qualifications to take on these positions. So do I. They are highly motivated and caring teachers and are willing to listen to and accept advice from their peers and leaders. Whether or not they are exceptions to an undefinable rule of thumb is something that I can't determine.
If I were a parent of a child for whom I had paid an enormous tuition though, I doubt that I would want just any John or Jane Doe teaching my child just because they can speak English.
Sometimes I think that it would be a good idea for China to establish a system similar to Japan's wherein recent graduates from English speaking countries, or even current students, are hired as assistants to the teacher. Of course this still doesn't solve the problem of the private schools hiring practically anyone off the street to "teach" their students.
But oh well, off to work I go - hi ho.