Actually, this is untrue; people automatically follow the rules of their language with extreme accuracy. They don't "strive" only in that following the rules doesn't involve any conscious effort.
This is behind the principle articulated for HTML of "be strict in what you emit and liberal in what you accept". That is how people behave when speaking. But it's not something they're capable of doing in HTML, and trying to apply it there was a mistake.
> Errors only matter if they create actual ambiguity; if you understand my intent, then I have used language effectively.
This isn't right either, in a couple of more serious ways:
First, ambiguity is always present regardless of whether any errors have been made or not. A fun example of ambiguity I noticed recently is "Flemish is more influenced by French than Dutch". Perfect grammar, but the two obvious parses have opposite meanings. Ambiguity arising from a grammatical error is no more serious than ambiguity arising from a lack of errors.
Second, the major problem with failing to follow the grammar of a language is that it prevents your audience from knowing whether they understand you or not. One thing I can say if you speak to me in broken English is that you aren't aware of the rules of English. Given that, even your apparently flawless sentences might have been intended to mean something quite different from what they would mean if spoken by an English speaker.