Even NASA have no clear calculations about moon's surface radiation, how should the "disbelievers" count it?
You can't count the typical Solar Wind and Cosmic ray dariation since it's reflective, unstable, and has changing sources.
The truth is, the Radiation type that we get on Daily basis is non Ionising, and bigger kind of wavelenghts.
Now, the Cosmic radiation OTOH is Ionizing and alpha,Gamma ray based. Many different kind of particles are just jumping, bumpin around on moons surface, and anythiny flying outer World's Magnetic Field get's the Bombardemend. 8 hours of constant X-ray exposure (On High Level) would kill anyone. it would burn tissues, change DNA source, cause mutations and whatnot. Cosmic ray is a much more dangerous/powerfull source of radiation! And with a Visible Bubble head protection, you won't have any way to get isolated from it!
If you read those articles clearly, you will see that even NASA doen't have that under controle. And they never had it 40 years ago!