If you want to be certain even though the above remarks have been stated, buy big bottles at your local grocery and pack them. When you go on excursions or into port you may have the opportunitiy to buy large bottles of water.
I tend to be a bit **** about the source from which water comes. My city tells me it is safe but we filter it and it tastes better. So if the ship says its safe I might take the same method to sea with me.
I imagine that they get sea water because they have huge desalination plants aboard the vessels. I can't comment authoritatively on the filtering process. My attitude, (right or wrong) tends to follow the idea of drinking the water from the bathrooms on airliners. I simply don't. (and I am not referring to just the "blue water!" either)
Actually, to remove all nervousness regarding water on board, I chose to enjoy highly distilled and peat-fired grain beverages. oh, and of course the bottled water. Jameson Irish Whisky! I was such a lover of Scotch until I tried it. As I ramble on, try a drink that I call "Warm Summer Day" Jameson and Sierra Mist or 7.