It's nothing like driving a real car on a real road.
A sim may be good but it's still a game.
On the road you have to be aware of so much more as the consequences are far greater if you get it wrong. You have to respect other drivers, pedestrians and other things that can and do happen in front of you (like animals, footballs, appearing from nowhere). You have to think about the weather, time of day, road conditions, deposits on road (debri, diesel, potholes, painted markings, speed humps. Chicanes, parked cars, kids running from behind ice cream vans etc). You have to consider weight and weight transfer and how it can effect braking, acceleration, cornering etc. You have to be aware of rules and laws in regards to speed limits, traffic lights, signs, vehicle condition.
I regularly drive VERY fast on public roads (legally I might add) and it is worlds apart from driving fast on a sim).
You drive a car with your body, you feel what the road is doing through your hands and senses and feel inertia and how to play the clutch. In real life driving you have to be far more aware of your surroundings.
A driving sim/game may sharpen reflexes, but so will playing Call Of Duty.
Having said that, it's still the closest thing you can get to driving whilst sat at your desk in your computer room.
As for people who play driving sims being better drivers, could that be because they have an interest in driving (or they wouldn't have bought a driving game in the first place) and therefore if you have an interest the chances are you are going to be better than someone who doesn't have an interest at all?
It's the same the other way. I am a very good driver on the roads but mediocre on a sim.