They do that with the Honda CBR125R bikes with race rubber. I may be wrong, but I read they do that because the front wheel's biggest load comes from braking, not putting power from the engine down to propel the bike forwards. The body of the rear tire is constructed to tolerate acceleration in a certain direction. Therefore, they turn the rear tire backwards when installed as a front tire.
Usually, we can find distinct front and rear tires from the manufacturer, so we don't have to reverse direction of the tire.
edit: the CBR race tire is Pirelli, but it comes in a rear-only size