While I do believe it would be highly classified, and for a long time, not subject to routine downgrade of classified material, I do not think it unlikely at all. There is not a lot available in print regarding naval operations during the Korean War, but what there is suggests that Soviet submarines were nosing around the area with great frequency.
When a submarine approaches a task force, there probably are not a lot of questions being asked about the identity of the crew, or the country that crew and submarine belong to.

Just my view of course. I am not in a position to either verify or discount the story, and it is quite likely, in my opinion, that no one else is either. You fellows still have the Official Secrets Act, and from what I have observed, that Act means what it says.