If anyone has doubts about the second claim, think about a hash function. The input certainly causes the output, but they are not correlated in a statistical sense.
Consider another medicine which kills everything with kidneys, unless they have a liver (eg., which filters it). Now there is no correlation at all with an effect on the kidneys, nor will there ever be (since all animals with one have the other) unless someone deliberately impairs a liver.
It also necessarily increases the incidence of other causes of death, as those who won't die of Alzheimer's will die of something else instead.