Not true.  The radiation levels on the surface of Mars are around 230mSv/yr.  The radiation levels in Ramsar, Iran, are 260mSv/yr.  That's not because Iran has been doing all kinds of weird dirty things with nuclear material, that's just the natural background radiation level there.  Want to know what issues they have living in such a high radiation area?  Absolutely nothing.  It actually has a *lower* cancer rate than the average.  Our preferred model for determining how much radiation is safe for nuclear workers assumes that there's a linear relationship between how much radiation you receive, and how likely you are to have negative effects.  It assumes that that's true no matter how spread out the dose is.  The model says
- If one person receives a dose of 1kSv, 50 people will get cancer.
- If 1,000 people receive a dose of 1 Sv each in one second, 50 people will get cancer.
- If 1,000 people receive a dose of 1 Sv each spread out evenly over the course of 100 years, 50 people will get cancer.
- If 1,000,000 people receive a dose of 1mSv, 50 people will get cancer.
- If 1,000,000,000 people receive a dose of 1Sv, 50 people will get cancer.
It's a clearly, ridiculous model that doesn't in any way represent reality. In reality, you need to tie an individual's dose rate, and total dose to their risk of health issues.  When you do that, you discover that below about 60mSv of radiation exposure health outcomes are actually better than baseline.  The amount of radiation that we have actual solid evidence causes problems is 100mSv in a single exposure.  That's. far far higher dose rate than anyone on Mars would experience
All that is to say, the radiation levels on Mars certainly are elevated, but they're not elevated to the point where our body can't handle it.  The dose rates are low enough that it's likely people will have absolutely no ill effects, and may even have some small health benefits.  If there are issues, there's a really easy way to deal with it - build your shelter underground.
There are some problems potentially with the trip *to* mars where radiation levels are around 1Sv/yr.  Of course, we do have solutions for that.  The steel sheet on the outside of the ship alone will attenuate radiation levels by about 10%.  Wrapping the water storage around the outside of the ship, assuming a 20cm thick layer of water, around the ship, you're going to get attenuation of around 87.5%.  With just those two, we've reduced the dose rate to around 100mSv per year, which... guess what... Perfectly fine.