A Much Easier Solution: "Filtering through earth removes essentially all of the fallout particles and more of the dissolved radioactive material than does boiling-water distillation, a generally impractical purification method that does not eliminate dangerous radioactive iodines. Earth filters are also more effective in removing radioactive iodines than are ordinary ion-exchange water softeners or charcoal filters. In areas of heavy fallout, about 99% of the radioactivity in water could be removed by filtering it through ordinary earth." Nuclear War Survival Skills Handbook http://www.oism.org/nwss/s73p919.htm go to 'Removing Fallout Particles...' to see more.
Question Time
Did Bethesda do enough research for the main questline, do you think? Or, did they assume that fallout was extremely hard to filter out of water?
Opinion Time
I think that Bethesda got kind of lazy with their research (I still love Fallout 3); I thought before I read that handbook that their wasn't a simple solution either, but it was easy enough to find out.