I completed this shop one week ago. I also spoke to the scheduler about the ambiguity in the instructions. I too have completed multiple credit card inquiry shops and have never been asked to sign a consent form. I asked to know specifically when a consent form would be introduced into the conversation. That question was not answered. I was told I could stop the shop when a consent form or social security number was requested. I was still a little uncomfortable.
I did the version of the shop where I had to be an existing member. I told the banker about my interest in a new credit card. She walked me through each of the available cards which fit my needs. She made a recommendation and asked if I was interested in applying for it. I said yes. She asked to see my bank card. I said I left it at home. She asked for my ID. I apologized and stated I wanted to discuss the recommended card with my partner first. A consent form was not introduced at any point in the discussion. I stopped the shop because I did not know what would happen once I handed her my ID or credit card. I was concerned she would run my social security number after I presented either one. The ambiguity of the instructions really left me with little room to do anything else.
I submitted the shop. It was accepted and graded.