If their safety programs aboard their tridents are anything close to the safety program aboard our tridents (which I suspect they are), then this is probably a bunch of BS by a sailor that just wants out of the military.
I always take these type of articles with a grain of salt. Disgruntled employee fueling a media wanting an anti-military bias. Questionable objectivity is most often the agenda.
Not saying that military safety is perfection and doesn't have flaws, but my experience with aircraft maintenance compared with the civilian equivalent was quite eye opening. The military has very strict procedural and safety standards. The civilian field does not have the same levels of safety. The term "military standard" is not just some catchphrase. It's a higher standard. What the civilian world considers airworthy, the military would not.
I know subs are not aircraft and there is no real civilian equivalent, but military safety standards are usually pretty high and applicable to all tech. When talking about nuclear weaponry, all the more reason to have even more extremely strict standards and practices.