While I'm not going to say your wrong, I would like a source to back those stats up. I'm not necessarily anti-union; however, it is in the union's best interest to say a particular work site is more dangerous than others when lobbying for increased benefits. Again, I'm not saying you are wrong....only that using an organization with potential conflict of interest as a source can lead to inflated stats.
That said, no one can deny the inherent risk of operating around nuclear materials and there will always be isolated incidents. Technology has also helped to decrease the risk.
Personally, I would have thought that the biggest danger to health on submarines would be sleep deprivation accumulated over the length of a cruise and the emotional strain of vitamin D deficiency which can push individuals over the edge.