I'm not sure how the 'dealer fit' roof bars attach, but the Thule (aftermarket) ones I've had for different cars over the years sit over the section between the top of the doors and the roof rain channel, and are held on by attaching to the inside of the door aperture. They attach just fine but I'm always wary of closing a door since the metal bracket is very close to the top of the door. They're also spaced quite far towards the centre of the car, thus there's only a couple of feet between them, so they're no good for carrying, say, a long ladder.
According to Thule's website, there's three parts to a Thule system for the Mazda 3 saloon: the bars (which seem to differ in length depending on which type of bar??), the rapid system to raise the bars in height from the roof, and the foot pack to attach into the door aperture. If you already have the first two items (and the bars are the correct length) then all you should need is the foot pack.