Do you agree not running is the safest way to heal a running injury?

I was just lecturing at the International Foot and Ankle Foundation meeting in Seattle. I was giving talks on running injuries. A doctor in the audience asked me if "not running" was the safest way for runners to heal running injuries. Keep in mind, this was a doctor asking the question. Have you ever thought this makes sense? After all, if a runner gets a running injury, and they stop running, that's the safest way to get it to heal. Or is it? Do you agree that not running is the safest way to heal a running injury? Well, that's what we're talking about today on the Doc On The Run podcast.