I keep feeling, though, that there is something quite intuitive about Aristotle's division. Consider the following sophism:
God knows temporal things, therefore God knows things temporally.
This may be a language-based fallacy, i.e., someone may make the inference primarily due to confusion about language. But it may also be a reality-based fallacy, i.e., someone may make the inference primarily due to confusion about the nature of time (or knowledge). These are two very different fallacies, similar as they may be. They both involve confusion about language, and they both involve confusion about reality; but one can have a linguistic resolution, while the other cannot. I'm not sure if this entirely carries over to Schreiber's issue; but it seems, just prima facie, that something similar may be operative here. It still might not save Aristotle's position (Schreiber gives several different arguments for his position), but it might explain it.
Or then again, maybe not; I certainly am no expert on Aristotle's text.