There will always be a morally correct option, because one of the options will be the one that "should" be taken. If you can be in a situation where EVERY option is morally prohibited, then there must be a contradiction of some sort within your moral code. A set of moral rules that are logically impossible to obey is a useless set of rules.
So in this universe, there is an unbreakable law that states that morality, a subjective term, will always have a back door so that people can avoid being guilty of anything.
Charming.
In the given example there are two options:
1. Murder some people. This greatly increases the chance that others will survive. - Murder is morally wrong, therefore this is a morally wrong choice.
2. Do nothing. Everyone will most likely die. - There is nothing morally wrong with people dying in an accident. By itself this is not a morally wrong choice.
The captain has the direct power to prevent deaths. He has more than enough reason to protect innocent lives. Him not doing so is morally wrong because he could have deprived more people the right to live than was necessary. You don't seem to understand the necessity of some humans dying (from what I observe) so that others may live, you simply see death as an unavoidable and regular part of any situation, and thus has no real impact, and trying to prevent it isn't as large an issue as some make it out to be... You're wrong (in my opinion). Preventing death is the most important thing to do, in my opinion.
Allowing others to die is morally wrong IF you have the option to save them (otherwise you are not "allowing" them to die at all, they are just dying). However, if the only option that allows you to save them is in itself morally wrong, then it's not really an option from a moral standpoint, and thus you have no option to save them, and are no more responsible for their deaths than you are responsible for the death of a pedestrian hit by a drunk driver. Put in another way: saying that "you are morally required (not physically required, morally required) to make an immoral choice" would mean an illogical and impossible set of morals.
The captain is obligated to protect the lives of his passengers, as far as I understand. So, he's actually not doing his duty, by standing by indifferently as the people he was entitled to protect die off. I would hold him accountable. It's really not up to the universe to decide what is morally wrong and right: it's up to us. We should be able to realize that what he did SAVED lives. Yes, he murdered, but if murder is just 'another means to die' then he was left with the following:
Let 21 people die (I think that's the number in the scenario)
or have 7 people die.
Every human life has a potential of its own. Depriving ANY potentials is wrong, but depriving ALL potentials is worse.