It largely depends on the circumstances of the original act. For instance, shooting someone under any circumstance is a very serious crime. Even if wasn't an immediately fatal injury, and it was totally by accident, there are still numerous charges that you would net: assault with a deadly weapon, criminal negligence, and so on. Some states even have laws on the books which allow cases that may not normally be considered murders to be treated as such—for example, the concept of "felony murder," where if you commit a felony that directly results in someone's death, even if you did not intend for it to happen, you could still be charged with murder.

Also, it depends on the circumstances of the death. It wasn't as if Brady had died in an unrelated incident that may have been exacerbated by his condition, he died as a direct result of the condition and the toll it had on its body. A more fitting analogy would be is if someone deliberately pushed you off a high ledge, you broke your spine, and you died 25 years later because of your paralysis.