An important thing to realize is that quarters is no longer a mission type in the book. So applying 6th ed scoring, denial, etc rules to them is sort of problematic to start with.
That's not advocating either position, I just important to realize that you can't take the BRB as gospel on this because it doesn't really apply. Table-quarters are largely a tournament-construct these days, and require house-ruling by their nature.
NOVA let no vehicles score quarters, so you saw basically vehicle-less lists. Battle for Salvation is NOVA-like, but 1/3 of missions Fast scores (like scourging, from the book) and 1/3 Heavy does (Big Guns) so it's kinda half&half. Feast of Blades on the other hand, vehicles never score objectives, but count for quarters just fine, while Flyers do not.
Point is, it's all over the place. Precedent, there is not.