Hey Al, shutoff valves don't always 'shutoff'.. You may have a water supply valve that's defective... Of course that doesn't answer where your leak is coming from... A flashlight and some investigating is necessary to determine your problem... I once found a bad condenser fan motor on a fridge that ran the compressor so hot it melted the water supply line for chilled water fill in the freezer door... Go figure that one out, even with water inside the plastic tube it melted... I guessed that the tube which ran right over the top of the compressor and it in turn ran with 300°F+ temps without a cooling fan was hot enough to melt the tubing... The customer had water on the floor whenever they used the water fill option on the freezer door...
The other probability is a missing condensate pan, I highly doubt that altho nothing surprises me being in this field of service repair... A couple of years back I walked in to service a fridge that had a nice round 10 inch pattern of birdshot in the right side... The elderly owner just smiled and quietly explained that the year before his wife had reached for a shotgun in the closet which fell and went off.. He didn't want to say that too loud where she could hear us..
Well my visit found the compressor done for and the fridge was ancient enough that I suggested it needed a trip to the target range just so she could finish the job...