Bummer, but its true you get what you pay for. Can you rehang the cabinets 4" away from the back of the wall and install a 4" filler to close the gap. This would bring the face of the cabinets in line with the front of your fridge.

I don't think the doors would have room to open if the cabinets were any farther forward.

The doors and refrigerator wouldn't move, just the cabinets around the fridge to flush everything out. The other is option is to build a box out of the same material to hid the sides and top of the fridge, but if you do this be sure you leave enough room for the fridge to ventilate.

This is the problem.

The counterdepth, while nice, is not the same thing as a unit intended to be built-in and will not yield the same results. The door on the counterdepth is a certain thickness (in addition to the cabinet panel on the front) and it must extend beyond the surrounding cabinetry far enough to allow the hinge to fully pivot. You can pull up the specifications and installation requirements of the particular Kitchenaid model that you have and there will be information and diagrams in those to tell you what the clearance requirements are. I don't see that the installer or whomever did this, did anything other than what would be expected with a freestanding unit. I think this is more of a misconception of what the unit was going to look like when finished.

Does the electrical receptacle and fridge plug push this out? A thought is to wire a receptacle in the cabinet above like you would for a microwave cabinet, drill a hole in the bottom of it, feed the chord up into the cabinet and plug it in there. You may pick up another inch which may be all you need to make this less obtrusive.

First question is, if you could move the frig back to the right distance would the doors open? If that is yes then how many inches does it have to move back. Is the wall behind the frig a supporting wall? What is on the back side of the wall. I am trying to see if we can put a header somewhere above the frig and changing the wall to less than the normal 4.5 inches to 1 or 2 inches. This depends if there is no large pipes in the wall and a open space on the other side of that wall.