Wow. I'm sorry that happened. I would be livid... can you read over their confidentiality forms again? I've only had my emergency contact called when I was being hospitalized and not in a state to make the call myself. There was one time the clinician told me they would call my wife and I denied them permission. At that point, they couldn't make the call anymore...
I'm not sure how likely you are to speak to that particular counselor again, but perhaps you can speak to the supervisor? I would probably approach it in a way that acknowledged how helpful the walk-in had been, but the call to the emergency contact made it feel unsafe to return (or something like that)...
:/
I'm glad your cousin is supportive though... I hope this call from the crisis Center didn't mess with that.