Personally I think it should be this way for both Crim & Gov. You just got revived by a medic probably because you got shot. You wouldn't get up and get back into the fight, you would go to the hospital, or seek medical treatment.
+/- Support
But crims have the chance to run. It's their fault if they do not take that chance and leave the scene. When it is code 4, the medic will start reviving, it's up to you to leave.