When we use the introduction of an alternative cause to weaken an argument, we are looking for an alternative cause to one of the observed effects used as a premise for the conclusion. For example, if I make the argument that it recently rained because the sidewalk is wet, then you could weaken my argument by pointing out at the sidewalk had just been washed. You are introducing an alternative cause to an observed effect, namely the wet sidewalk.
We are not looking for an alternative way to cause the desired effect. This would only weaken the argument if the conclusion had been, "The ONLY way to improve public health is..."
