Not sure how to address this. NASA obviously knows whether or not they have the means to deal with cosmic rays, and it's not been presented as a major stumbling block in any of their manned Mars proposals thus far, so I assume they have a workable solution in mind. I've certainly heard a number of workable solutions presented in the past, so don't think this is a problem. Still, I imagine it gets mentioned in a lot of science/educational shows, as shows of this sort often exaggerate the danger, as it makes for more exciting and memorable television. The Discovery Networks (of which The Science Channel is a part) are especially guilty of indulging in blatant sensationalism.
And the gravity issue is pretty much moot as well, as you've presented the obvious solution (a centrifuge of some sort) in your post.
The only stumbling block you've alluded to, which I believe has any real merit, is the political aspect of funding the mission.