Thanks for the contributions and ideas. I stopped by my AS on the way out of town this morning and looked closer at the interior. The freezer compartment seems to be well sealed as I poured some water in it and it went nowhere.
The drain pan was in the correct position and the drain was correctly placed over the funnel that leads to the plastic drain tube exiting out the rear of the refrigerator and discharging at the lower vent door onto the ground. Water poured into the tray drained properly with no leaks.
Since the drain tube is at a lower level than where the dripping is seen in the rear compartment I figured it had to be something else. Closer inspection of the area just beneath the metal fins shows what I suspect is the problem. The attached picture will help clarify, but the white plastic skin that makes up the interior of the refrigerator is not sealed well just below the metal fins. There is what appears to be some kind of expanding foam that might serve a dual purpose as an insulator and a glue. The white plastic pulls away from this area easily which means there really isn't a good seal. When the refrigerator is turned off, the ice melts and drips down the fins and the back plate. Water dripping off the fins
goes into the drain tray and exits properly. However, the water that drips down the back plate
doesn't make it to the drain tray and instead seeps into the poorly sealed section at the base of the plate. It escapes through the seam in the rear compartment shown in the previous pictures and collects on the floor of the refrigerator compartment. Not good, of course.
Again, thanks for the thoughts and suggestions. I think I've gotten to the bottom of it. Next challenge will be to see what will be done to fix it. The refrigerator is under warranty. It will be a year since I took delivery on 11/4/2011. I believe the warranty is longer than a year -- don't have the paperwork with me right now.
I don't doubt the seal can be fixed. My concern is about water that has seeped into an area where it shouldn't be. If my understanding from other posts here and on other forums is correct, when water collects around the interior metal tubing it can over time cause the tubing to rust leading to leakage of the ammonia cooling mixture. If my warranty is 3 years (I think?) I'm not sure this problem would manifest in that time frame and I'd be hung out to dry in, say, year 3.5 when the coolant leaks. Warranties are scientifically analyzed and timed to work that way, right?
I'd love for the entire unit to be replaced but am I being extreme?