"The toxic seawater was sucked into the ship’s desalinization system, flowing out of its faucets and showers — still radioactive — and into the crew member’s bodies."
A Nimitz class carrier can produce somewhere in the neighborhood of 400,000 gallons of desalinated (potable) water a day. Desalination is very energy intensive, but energy is something that a nuclear powered carrier has plenty of. There are obviously some consumables involved, but it's mostly just energy, and lots of it.
RO, on the other hand, requires a lot of high quality, small pore filters and membranes that need to be cleaned and changed regularly. RO systems have dramatically lower throughputs than desalination systems of similar size. An RO system capable of producing 400,000 gallons/day (especially one capable of filtering radioisotopes that are (while larger than a water molecule), still quite small) would be very large, and very maintenance intensive.
But hey... you're probably right... The folks who designed the potable water infrastructure for the Nimitz class aircraft carriers were probably idiots...
You are not an idiot just for doing something stupid. All people, even the smartest ones have capacity to do dangerously stupid things. In this case they probably just weren't ordered to built a system that can provide clean water in case of the ship being covered in radioactive snow. So the people doing stupid things (possibly, but not necessarily, idiots) were the people who gave orders. Still hard to imagine for a country that treats nuclear war sort of seriously.
Of course I think you are totally right about RO being non-easy. I have no idea about RO and desalination systems but my motto is "nothing's ever easy".
I think it's even more likely that they weighed the advantages and disadvantages of each system, and decided that a waste heat desalination system would be a _much_ better fit then a huge, expensive, high maintenance RO system.
My point was simply that this was almost certainly an informed decision, not an oversight (or just 'following orders').
(It also seems to be a possibility that they were using (contaminated) seawater for decontamination procedures, but that is hard find reasonable information about)
http://www.gao.gov/assets/660/657412.pdf
RO is already used in utility-scale desal plants:
http://www.pub.gov.sg/water/Pages/DesalinatedWater.aspx
"This plant can produce 30 million gallons of water a day (136, 000 cubic meters) and is one of the region’s largest seawater reverse-osmosis plants."
If you're trying to minimize energy (particularly steam) usage, then RO starts to make a bit more sense. On the Nimitz class, they have plenty of waste heat from the powerplant, and already had numerous steam distributions systems in place.