Yeah cause Rick sure as heck wouldn't have done it. That's already enough to show he's a softie compared to her. Until he does something dramatically convincing enough to show he's got balls again, Carol will remain tougher mentally than him.
No, he wouldn't have done it cause the others in the group are still trying to figure out the illness.
I got it, let him walk in the prison & kill everyone who coughs. That way he'll make you happy.