You're right about most of it, but companies by AdWords on their own brand name so that competitors won't get that spot. Basically, the first 2 results listed by Google are paid ads. So if they don't buy AdWords for their own brand the top 2 displayed results could be any similar item. So that case isn't about increased conversion, it's about not letting competitors snipe their sales by offering a lower price for a comparable item even when searching by brand name.