I "made" potable water during my Navy career - running the evaporators which distilled and purified seawater into drinking water. It was quite safe to drink and as others have said it is probably of higher quality than the bottled stuff. Also - although ships have evaporators they also take water on while in port. So it is likely that a ship leaving from the Port Of Miami has a good amount of the local drinking water in the holding tanks - although they also filter it while pumping it aboard and also sample it for any impurities or organics.
I never buy bottled water on a cruise, and have never had a problem with the tap water.