"Cosmic rays, they claim, maybe a "showstopper" for any manned missions to Mars.
The science article states that astronauts living onboard any thinskinned spacecraft
for a year, beyond Earth's magnetosphere, will have one third of their DNA destroyed."

Couple points. First, I suspected this would be problem. Second, it "seems" worse than I thought it could be. Third, we still don't know yet.

Additionally, if a third of DNA is destroy in one year then how much is destroyed in 6 months, 2 months, 1 month [1/6th, 1/9th, 1/18th?]. And one's cells are normally replaced- for instance IF a 1/3 of all human cells died "normally" within couple years it wouldn't be surprising to me [I don't know the number off hand- I imagine it depends upon the person and age of person]. And I *guess* what's more important is damaged cells and WHICH cells are damaged or destroyed.

The other aspect is it's probably possibly to do Manned Mars even if worse case. You going to have to have a solar flare shelter in almost any proposed Manned Mars- because Solar flares can't be predicted with enough certainty and solar flares can simply kill the crew if unprotected. So if crew merely sleep in the shelter for 1/3 of the total time, this simple and obvious measure effectively decreases the trip time in terms of radiation recieved.
But also more along this line, it could possible to make all the living areas sheilded from cosmic rays: If you plan to get to Mars fast [less than 6 months] the faster you go increasingly requires that bring enough fuel to brake [or even change course] so you are slow enough to safely use Mars' atmosphere for capture. If you are bringing lots of fuel, you are bringing lot's of sheilding.
Another route which solves this is by going fairly slow, but use cyclers [motherships or just very small asteriods which put into a Mars-Earth Orbit and manned craft docks then undocks from them.]