Well yassa I am impressed, You seem to know more about the Van Allen belts than James Van Allen did!
He dismissed this idea.
They got quite a small dose.
However they were lucky - if there had been a major solar erruption whilst they were in transit they could have all been killed whilst they were outside the Van Allen Belts. The odds of this on a quick trip lasting only a few days were acceptably small.
Spending a year on a trip to Mars is substantially different!
All the old conspiracy theory questions and answers are tired so I won't go into them - you know them as well as I do.
But the best proof I know of the landing is the laser reflectors left on 2 of the trips - generations of physicists have used them to measure the distance of the moon to tiny distances.
http://science.nasa.gov/headlines/y2004/21jul_ llr.htm
This French group use them extensively
http://wwwrc.obs-azur.fr/cerga/laser/laslune/e nglishintro.htm
Are the French in on it too?