The first question has to be what he understands by the term 'radiation'. Many people, especially those who see it as a relevant concern in the Apollo hoax idea, think of radiation as some big, all-penetrating thing that makes you sick and kills you. What few of them, in my experience, realise is the wide variety of kinds of radiation that exist, and hence that an argument that just talks about 'radiation levels' is meaningless and inconclusive. Light and heat are also forms of radiation.
The VAB, for example, is not actually protecting us. The magnetic field of the Earth does that, and in trapping the particle radiation from the solar wind it creates the VABs. Of course in trapping those particles it makes the VABs a region of high radiation, but it's particle radiation. A lot of that can be blocked, or at least attenuated, by spacecraft hulls and insulation, and as it's a belt it can be avoided almost entirely. Some of the EM radiation can be blocked by a spacesuit. UV radiation, for instance, can't penetrate a white spacesuit or even the clear polycarbonate of the helmet. It doesn't matter what the radiation levels in space are if you happen to be encased in something that can reduce the exposure significantly anyway. His 'logic' is based on a very shaky premise.
He should also consider that we have decades of data about the radiation levels in space, a significant amount of which is important for commercial revenue. Satellites are just as susceptible to radiation as humans (more so, since a human body can repair itself while satellite electronics cannot), and we depend on them these days for communications, GPS, and so on. Does your friend honestly think he's the first person to look at the data and realise it exposes a hoax of the scale of the Apollo program rather than people who understand the subject realising it does no such thing and so maybe he should take that into consideration?