I am completely sure, that one to be part of language instructors must have studied. This is because teaching a language is pretty complicated and required a lo of knowledge in order to make our students acquire the new language. Imagine that because I am Spanish native speaker I am prepared to teach my mother tongue as a second Langauge. Example, I travel to another country where people speak English as their native Language, so in that country i get a job to teach Spanish. Do you think I have the proper knowledge to instruct people?.
Do you believe, that because one as a native speaker can teach a language without being trained firstly?
Well, it depends. It depends on the age group you are teaching, the level you are focusing on or are you preparing them to nail any particular language exam.
It's different when you are teaching any language because most of the time teaching is dependent on the way you are handling doubts, the class activities you are making them to participate.
So my opinion, a non-native speaker can be a good language teacher and even a native speaker without any proper training can fail as a teacher.