You guys screwed up. Congratulations. Read the whole context (which you provide) and it's ambiguous -- he very well may be referring to nuclear-powered AIRCRAFT CARRIERS -- which they don't have yet. Also, during Vietnam, Cain was working ballistics for the Navy, studying the range and capabilities of China's missiles. He knew they had nukes. It was inartfully said. Not a mistake. According to your own rules, you don't fact check things like this: "Is the statement significant? We avoid minor "gotchas"’ on claims that obviously represent a slip of the tongue."That about says it all, but I'll just add one helpful informational link.
Given the ambiguity of Cain's statement, it speaks volumes about PolitiFact's ideological predisposition that no attempt was made to interpret Cain charitably.