Water is not remotely as good as lead is by mass as a radiation shield. If you aren't already hauling many cubic meters of water for other reasons (and you wouldn't be), it absolutely wouldn't make sense to bring it along solely for that purpose. Water also has the severe problem of being liquid at habitable temperatures, so you either have to continuously spend energy to freeze it or deal with absolutely ruinous slosh.

The linked article is talking about the radiation shielding properties of what essentially amounts to a large swimming pool's worth of water. You know how much that would weigh?? Water is not a good radiation shield, it's just cheap here on Earth, so we use large quantities of it in applications where weight doesn't matter.