Yes, it's quite true that learners of English do not need to study the rigors of grammar to be able to speak accurately and fluently. With the current communicative method of teaching, students can learn grammar through games, role-plays, word-substitution exercises, and other various forms of activities.
But as teachers of English, I believe we can be at an advantage if we know how the language we are teaching works. Equipped with the essential knowledge of phonology and syntax,we can do the following:
1. correct mistakes of students more efficiently
2. develop techniques to teach students how to manipulate the language
3. be more creative in the exercises or activities that we develop to raise the student's level
Thus, it is not the conventional teaching of grammar (i.e. sentence diagramming, enumerating parts of speech, etc.) by English instructors that is relevant to a student's learning how to speak a language. It is the firm knowledge of grammar by English instructors that is relevant to a student's learning how to speak a language.
Just as an accountant wouldn't be able to complete an accurate financial statement without knowing the rigors of calculating for depreciations and cash flows;
Just as a financial analyst wouldn't be able to give sound business advice to his corporate client without knowing the rigors of price/earnings ratio and asset allocations;
Neither would an English teacher be able to effectively teach without knowing the rigors of English grammar.
Well, these are just my thoughts on the matter based on my experience as an English teacher.