Yeah, a car (yeah, road car, with doors) with open roof can never be as light and rigid as a car with fixed roof. My mechanics of materials professor demonstrated this really well. Take a hard plastic tube and try to bend and twist it. It should be pretty unflexible. Now take a knife and make a transverse cut about 80% deep of the radius. Try to twist and bend it now. It's wobbly as hell, and you barely removed any material. You've just created open-top plastic tube. If you've ever opened both doors in a cabriolet, you've probably noticed there's only the floor keeping it together. Floor is also pretty flat part of sheet metal, which is not very rigid. Floor plus roof on the other hand is.
But S2000 demonstrates, a open top car can be rigid, but at the cost of additional weight. It can be minimized by clever design, just like Honda has done, but it's still heavier and less rigid than S2000 coupe could be. Do we care if it's well made? Of course not.