Actually, in a sense, yes. In the end, it's the HAC's call, but usually SOPs state to make an effort to get permission from the CO first. If the CO doesn't feel that's been met, or just generally wants to say it was a dumb idea, he has that right, since he's signed the HAC's papers.
At sea, contacting the CO may be as simple as trying to get whomever's controlling you the info, relay if needed, and go from there (ship's CO, E-2, P-3, etc).
Did these guys do the wrong thing? Well, apparently the skipper thought so, but I'm sure the rescuees would disagree.