Responsibility is a nebulous concept. The extent to which a clinically depressed person (if indeed he was) can be said to "be responsible" for their own suicide is pretty debatable.
Supporting your (hypothetical reasoning, yes), I'd rather say that it is in most cases inexistent (at least from a relevance point of view): the urge can be so overpowering that 'responsibility' becomes almost meaningless.
That is why support is so so so so so so so important.
