They had the equipment to perform surgery and remove the bullet inside her, but needed blood for Jane to have any chance at surviving surgery.
Weller screwed the team over a little, but really, it was a collaborative effort between him and Rich.
While Kurt was getting tortured, Rich, Patterson (whose first name was revealed earlier this season) , and Zapata were trying to save Jane’s life after she had been shot.
Zapata was ruled out as a donor when she was forced to reveal her pregnancy to Patterson and Jane, but Rich said he knew a blood guy and rushed off to find him.