Best thing to do when someone blows is to let them blow. Don't try to calm them down, don't try to cut them off, or tell them why they are wrong or anything else-just let it go.
Eventually they wear themselves out. Then tell them what if anything you agree with from the tirade. Ask a few questions, and take it from there.
I agree that letting them blow is wise. But helping them pick up the pieces is also the caring thing to do.