Hmm I can relate with Chinese school, sounds like me and Viet school. Maybe a combination of methods of teaching? Immersion along with traditional textbook to reinforce the grammar. The textbook can counter problems with the immersion style, such as students continuously using incorrect grammar/phrases that natives would not understand, but the teacher, as a native English speaker, could, and so accepting it the student thinks it's okay.
I do agree that "natural" learning has a place in LOTE learning. I can see the problem with a language taught ONLY as a written language with grammar and vocab lists, and students not knowing how to maintain a conversation. This is most apparent in early education of a LOTE, where teachers tell the students to do some task such as "find out the hobbies of your classmates in X language". The students obviously cheat and use English.
This is what I think about LOTE. For first languages however, "natural learning" is inevitable anyway, it's probably more beneficial to teach the mechanics of language and proper spelling, phonetics etc.
On another note, have you ever seen Rosetta Stone software? They try to teach you a second language "how you learn your first language", without teaching any grammar specifically. I seriously think it is fail. That's an extreme anti textbook method.