I’d say they are closely related.
Broken limbs are lacking the necessary blood circulation. This leads to the body part cooling down quite a bit (can also be observed on player characters).
Having a hypovolemic shock of intensity of at least 2 (= Moderate hypovolemic shock) can lead to (temporary) extreme temperature dips of hands and feet (see related code).
At some point the body part might get cold enough that they take freezing damage on it, which in turn lowers the internal recovery timer (see list “Mending factors” at the end of my post in another topic).
In short: No, this is not a bug. It seems to work as designed.