[andreasvc]

> I doubt anyone reading "Alice drove down the street in her car" actually parsed the grammatical structure of that sentence, either explicitly or implicitly.

You do need to analyze a sentence to understand it. Think of a classical attachment ambiguity such as "the boy saw the girl with the telescope". There are two readings of the sentence, and just like a Gestalt, you're typically perceiving it as one or the other. This involves a process of disambiguation, which is evidence that you have parsed the sentence.