My guess is that since the term, "shot" is usually a firearms-related reference, they can't have the term 'shot' being used for a positive purpose such as a vaccine.
I first noticed this subtle word play many years ago in reference to "shooting" photos. I was into photography as a hobby and taking classes. I noticed that some of the more 'granola' types (I wasn't really politically aware at the time) would say things like: "We don't 'shoot' photos. We 'take' photos." Or "We don't 'shoot' people we 'freeze' them in time.", which I found to be even stranger.
Interesting and plausible.