Not just a factory recommendation, but a requirement. The cooling water that runs through the ski passes through jackets around the cylinders, and into the exhaust system. If you turn the water on without the engine running first, there is a fair chance that water could enter the engine through an open exhaust port. The result is a hydrolocked engine (bent valves, etc.), and potentially severe damange from the water if not removed quickly (rust corrosion, etc.). With the engine running exhaust pushing out will prevent this from happening.
The correct procedure is hook up the hose with the water off, start the engine, then start the water, after you are done, stop the water, then kill the engine. As far as I know this applies to all brands of skis.