Absolutely correct. The type of radiation was, at least in part, high energy particles, which would be somewhat attenuated or blocked by the spacecraft and space suits. The duration during the pass through the van allen belts especially was very short. The times of the flights were not during sun storms or other hazardous times.

The amount of radiation the astronauts were exposed to was relatively small, all things considered. It might be equivalent to getting a couple of x-rays and then taking a trans-continental flight.

In theory, any radiation exposure will increase the chances of cancer because it can cause genetic damage. In practice that small an amount is unlikely to have enough effect to really notice any increased probability, especially with such a small group. And it would be far too little for any acute symptoms of radiation sickness.