Whoever told you not to drink the cruise ship's water is misinformed or has not been on a cruise in many many years. All the cruise ships have water purification systems and the water coming out of your tap is as clean or cleaner than your bottled water.
If they meant the water in the ports, then yes, you do have to be carefull about that in some ports. You can take bottled water off the ship and we do bring some bottles for that purpose. You can buy bottles from the cruise line as you leave, but those are pricey. (Although if it means paying $2.50 for a bottle of water versus lugging your own bottles through airports, just buy it on the ship. We only bring our own bevvies if we are driving to the port)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013