What I feel with Chinese (and I think this applies to other languages too) is that there are two levels to [learning grammar]. There are sentences that are technically “grammatically correct” according to someone’s made-up grammar rules that seem to fit all situations, and then there are sentences that actual people say and that actual native speakers consider to be correct.Language Fixation is touching on two things here. The first is word usage, which I already addressed here, and the second is informal grammar rules.
Native speakers often seem to use the language in ways that seem to break the grammar rules included in most grammars. These may break the rules found in the book, but are they really breaking the rules of grammar of the language as they exist in the wild? You can probably guess that my answer is going to be no.
Let me start with an example. One day my wife and I were talking about how she and other drivers sometimes don't bother to pass slow cars, and I said to her, "Bunch of wusses, you all." What a grammatical mess, right? There's no verb, the subject is at the end despite English being SVO, and the subject pronoun "you all" is, according to Wikipedia, used "primarily in the southern United States and African-American vernacular English", even though I am neither from the South nor African-American.
The fact of the matter is that, even in situations such as these, grammatical rules are being followed, even though they may be informal rules that the authors of grammars don't always see fit to include. In the case above, this is a standard kind of interjection, which takes a standard SVO declarative sentence, such as "You all are a bunch of wusses", and makes it into an interjection: "Idiots, these guys!" "Disgraceful, today's kids!" "Geniuses, those people." And so on. We could go into more detail about how that construction works, but suffice it to say that these are following grammatical rules, even if some sticklers might consider a sentence like that ungrammatical. ("You all" is more of a word usage issue, so I'll refer you back to my earlier post on that one.)
Let's turn to Chinese for another example in the same kind of SVO reordering. "Nàge mǐfàn, wǒ chī" 那个米饭，我吃. You cold translate it as "I'll eat that rice". This would sound perfectly normal when spoken in Chinese, but most grammar books would probably tell you to write it like this: "Wǒ chī nàge mǐfàn" 我吃那个米饭.
The thing about informal grammar is that it's still grammar, even if those who write grammars don't see fit to put it in their books. So I'd agree; barring that you find a grammar with this level of detail, you'll need to get this from context.
A grammar stickler, as the authors of grammars tend to be, might wave this sort of thing off, calling it grammatically incorrect. I'd say that's the totally wrong approach. Grammar is not a box that a language is to be crammed into; it's a series of observations about how the language is used in practice. It's not about how it should be, it's about how it is. Or, to phrase it another way, it's descriptive rather than prescriptive.
And the "how it is" part includes both the rules that grammarians tend to include in grammars and the rules governing informal usages that are rarely included in grammars. Thus, in terms of rules, the gap between what a grammar teaches you and how native speakers actually speak is because of one simple thing; the grammars are incomplete.
So when people criticize grammars, saying that they don't tell you how native speakers actually speak, they have a point, and such grammar is surely better learnt through exposure; if authors aren't generally including it in grammars, then you'll likely have few other alternatives. That said, that doesn't mean you shouldn't learn what can be learned from grammars, even if you need exposure to cover these kinds of grammatical patterns. And, of course, if you can find a grammar that covers such rules for you, all the better.
So make use of grammars, but remember that you're almost undoubtedly going to find "ungrammatical" grammatical rules that were not covered in your (or, perhaps, any) grammar.