The audio lingual method is called the army method, because it was developed during WWII when large numbers of army interpreters had to be trained quickly. The method is based on the behaviorist theory of B. F. Skinner. The heart of the method is the drills that give the student an intuitive understanding of the grammar of a new language by conditioning--receiving rewards and punishments. The audio lingual method is the basis for successful modern language learning systems, like Berlitz and Rosetta Stone.
The audio lingual method of learning is based on the belief that we learn grammar at a subconscious level through conditioning. This is the way children learn their native language--repeated examples of grammar use imprints the rules on our language behavior. In an audio lingual class, the grammar is never explained in any language. Grammar is absorbed at a subconscious level. A sentence is grammatically correct because it "sounds right."
Teaching methods are never as pure in the classroom as they are in books. Methods must adapt to student and teacher needs. Methods must also adapt to expedient solutions instead of pedagogically correct ones. Teaching by example only is impractical in the classroom--there is simply not enough time. Audio lingual based classes will occasionally introduce vocabulary because not everything can be pointed to. In some instances (preferably during a summary) grammar might be explained in a non-target language.
As long as most of the class is conducted in the audio lingual method, the benefits are enormous. Students who are taught this way have an intuitive understanding of grammar--just like native speakers. It is only necessary to get this ability up to a certain critical level because thereafter every conversation in the new language is further training in the rules of grammar.
Remember that there are two sets of grammar rules: prescriptive (the language according to books) and descriptive (the way people actually talk). You should use descriptive grammar when speaking and prescriptive grammar when writing.