I received a reply from Winnebago. The customer service rep had this to say, "Looks like the cabinet was built while installing it". He needs to take a factory tour.
It turns out that the shelves are just framed. You can gently pry off the facing and then again gently pry off the top layer.
These parts are fastened with brads. If you're careful you can reuse the brads.
The shelves are fastened with four screws. The screws only attached the shelves to the back of the cabinet.
With shelves removed you finally arrive at the two screws that attach the cabinet to the wall.
This wall was built with boards that run laterally across the wall. It seems that they are spaced about 18 inches apart. Of course none were where I needed for relocating the cabinet. I ended up drilling a four inch hole in the wall so I could insert hardwood screw strips.
I glued the screw strips to the front and rear walls.
Here's the end result.
The faucet has a motion sensor. You can turn the water on and off by just moving your hand in front of the base. It's great when you're trying to conserve water.