Just yesterday Sue and I were sailing in light/variable wind, say 5 to 11 knots with main and 135% genoa. On a broad reach, boat speed was 2 to 4 knots. On a close reach, boat speed was 5 to 6 knots. The point of sail absolutely affects boat speed, particularly in light wind. There is no arguing over perception when you are measuring boat speed.
BTW, when on a broad reach, there was no heeling. When on a close reach, we were heeling even in the lighter wind. In gusts approaching 14 knots, we were easing sheets as apparent wind moved back to increase sail efficiency and to prevent excessive heeling and the resultant helm pressure. It's not an illusion that heeling is associated with speed. In this case, it's a fact. Speed increased with associated heeling. Of course, keeping the boat as flat as possible with an increase in wind speed improves speed, but let's not perpetuate a myth that heeling is slow.