In the same way that if someone at works cuts their hand off im responsible because im their supervisor
To a certain degree. If you are responsible for their training, then yes you will be probably not a trainer anymore. (demoted - that's called consequences of responsibility. its why the US military and Im sure many militaries stress training and doing it 'exactly" as instructed.
It's different on ships and especially military ships. Yes she is responsible for her 1st Mate, running aground. The Captain approves all charts, plotted courses and designs training and emergency exercises. So yes she should be demoted and bounced out in disgrace. She won't because woman and lesbian. That would be sexist and homophobic.
The fact that she approved a course that ran too close to the shoals seems to be completely lost on you. These shoals have been charted for literally hundreds of years.
Not to mention the complete failure in saving the ship, and the debacle of abandoning ship and the casualties the crew suffered during and after abandonment.
Generally speaking, it's seen as incompetence, if you capsize your own ship no matter if you are a private vessel or a member of a navy.