No, it's really not. The action that put the person in the hospital where they lingered for a month before dying either happened when it was legal to homicide, or not. Without that specific action, the victim would not be dead — or, more specifically, would not be in a situation that led to their death.

Criminal law absolutely recognizes that causal chains have a "first link", without which the rest of the chain wouldn't even have happened. It also specifically subjects the party causal to that first link to special scrutiny.