The original argument did not involve which trips can be replaced by walking or cycling, merely that per distance driven cars are safer. This makes driving a car much safer than walking, which should give us pause and make us reconsider if it makes sense. It doesn't -- merely having and regularly using a car makes people travel greater distances. Without a car they wouldn't do it, and increased car dependance results in worse traffic safety. If the US had the same per capita death rate as the Netherlands, there would be around 12k deaths. Instead there are over 40k.
The additional kicker is that most of the pedestrians and cyclists killed die after a collision with a car. As it is, roughly two million people in the world die in traffic per year, almost all of it involving cars. So much for safety.