If a man is without money and an opportunity arises for him to steal the medication his wife requires to stay alive, which responsibility is stronger, the one that says "don't steal" or the one that says "don't let your wife die"? I would argue that it's the latter.

You seem to be advocating that a responsible person must always abide by the law. I suggest that this is as doomed as Kant's Categorical Imperative to always tell the truth. The law should recognise when people are in impossible situations. Indeed, when it comes to self-defence as a means to avoid a murder charge, we already do. So, the man that stole the drugs to save his wife's life is analogous to the man that shoots the home invader to save his own life (and possibly his wife's too). But only one of those men will get away with it, and it's not the one that actually commits the lesser crime.

Can you present a principled reason why it's OK to murder someone when you think they might be about to murder you, but it's not OK to steal medication when you know (for a fact) that the failure to do so will lead to death?

I suggest that your excuse/reason distinction would work if we had a perfect legal system. But we don't. So, it's just a way to ignore people's plights and, further, to not do anything about resolving those plights in perpetuity. This gives rise to the question, "What is society for if we're just going to ignore those less fortunate than ourselves and entrench the injustices?"