Talbot, I'm not really sure what is expected in those situations, other than to say that motors (with and without impellers) should be run in freshwater after use in saltwater. How this is accomplished I suppose depends on the situation. The H2 is considered a "portable motor", so I guess Honda assumes (rightly or wrongly) that the motor will be removed from the boat and stored after use - at least that's what the literature I have points to. In the case of the larger motors that stay on the transom for the season, I suppose that they are to be flushed out using the "garden hose/earmuff arrangement". For trailered boats this would be done at home after a sail, for boats kept in a slip, you would use the freshwater connection (usually) provided.
The issue as I understand it is that the very same salt residue layer that you are observing on the underside of the cowling is also building up in the various cooling water ducts inside the motor/engine, and the only way to clear them out is with a freshwater rinse. Otherwise you are just asking for blockage and/or corrosion damage in there.
My (used) H2 (luckily) came with a Garelick motor stand,
http://www.garelick.com/Outboard-Motor-Carrier#, the 31400 model (something similar could easily be homemade), and after a salt water trip, I just put the motor on the stand, place a big bucket under it, fill it with the hose, and run the motor for about 5 minutes at just above idle (just enough to get the prop turning, but not so fast as to splash all the water out!). I basically run it with the fuel valve off until it quits. This way I know I'm storing it with the carb bowl empty, which I've also been told by several different H2 owners is a good thing to do. But, that's an entirely different discussion altogether ... ;-P