To reduce cutting edge nuclear weapons tests, at a time when the USA and USSR were neck deep in an arms race and at each other's throats, to a nothingburger about space radiation is... fantastic. How great is it that today we can live so ignorant of one of the scariest times in human civilization?
The everythingburger had to do with the orbital EMP, not the radiation or even the secret tests. If the US had developed an effective way to neutralize Soviet ICBMs with atmospheric detonations, it would have been the end of MAD and would have forced the Soviet Union into all out war in a race to beat the US before a full defense system could be built - at a time when they were first starting to come to the table.
The everythingburger had to do with the orbital EMP, not the radiation or even the secret tests. If the US had developed an effective way to neutralize Soviet ICBMs with atmospheric detonations, it would have been the end of MAD and would have forced the Soviet Union into all out war in a race to beat the US before a full defense system could be built - at a time when they were first starting to come to the table.