This has come up several times in the Navy-nuke Facebook group in which I lurk (I used to be one of them). The posters in that group have been, shall we say, scathingly skeptical of these claims of radiation sickness. The group includes a number of current- and former radiological-controls specialists, known as engineering lab techs or "ELTs." Navy-nuke ELTs are a select lot who are trained to face the facts and tell it like it is. As a general rule, they're very good at spotting BS, and they're not especially inclined to just passively accept it when they do spot it. Their skepticism about this radiation-sickness story is worth taking into account.
EDIT: Consider some circumstantial evidence:
- In the Navy nuclear-power subculture, people pay attention to detail (to put it mildly). This is true in general, and especially on the subject of radiation exposure to the crew or the public.
- The commanding officer and executive officer of every U.S. aircraft carrier are nuclear-trained, on top of being senior aviators or naval flight officers; they must successfully complete the full, one-year, very-intense nuke qualification course even to be eligible to hold those jobs. Then before they assume those jobs they undergo still more training to be an XO and then CO.
- On any U.S. aircraft carrier, the chief engineer (who "owns" the evaporators that produce the ship's drinking- and washing water) and the [chief] reactor officer (who "owns" the ELTs) are nukes, of course. They're among the most-senior officers on the ship.
- Unambitious people don't put in the years of stressful work that it takes to get these jobs. It's a safe bet that these senior officers all want to be admirals someday. A radiological "incident" of the kind being described likely would severely impair their chances of ever being assigned to a responsible job again, let alone being promoted to flag rank.
So: We're being asked to believe that, in a non-combat situation, somehow all of these career-minded senior officers aboard the Reagan inadvertently allowed the crew's radiation exposure to get to dangerous levels. Sorry, I just don't buy it. I suppose we can't categorically rule out the possibility, but to me it's another reason to be skeptical of the radiation-sickness claims.