RegUS PatOff is on the right track. Sub-Zero's are notorious for leaking evaporators on the refrigerator side (almost NEVER in the freezer though). The evaporators are made of aluminum. In the freezer, the temp is so cold that the various salts and whatnot from your food don't corrode the aluminum. In the refrigerator, the temp is 30 degrees warmer than your freezer, this is just enough to where the chemicals and salts from your food can slowly corrode the evaporator, eventually causing it to leak (usually 10-15 years after purchase).
This never happens in other brands of refrigerators because practically no other manufacturer puts a separate sealed system and a separate evaporator on the fresh food side. This is unique to Sub-Zero refrigerators (with a few oddball exceptions).
Post a picture of your refrigerator side evaporator and we'll try to confirm whether this is your problem or not, but i'm putting my money on the evaporator.