Clara wasn't only saving her friend Rigsy -- she was saving the young man who had essentially acted as Companion to Doctor Clara in Flatline; in other words, exercising the due "duty of care" the/a Doctor assumes over his companions. She was also trying to make sure that Rigsy's infant daughter wouldn't have to grow up without her father's presence. Clara, after all, lost her own mother, so she knows a bit about that.
YOU BETTER NOT JUST BE TEASING ME. I WILL KILL YOU IF THIS DOESN'T HAPPEN. I REALLY WILL. DO NOT UNDERESTIMATE ME. IF HE DOES NOT COME BACK YOU ARE SOOOO DYING. A SLOW AND TORTUROUS DEATH. DON'T PRETEND IT CAN'T HAPPEN. IT DID IN THE THREE DOCTORS.