Legally speaking, though, there has to be a "meeting of the minds" and consensus of terms. I have seen a short application and no terms. I have not agreed to any terms, I agreed to provide information for consideration of my application and I agreed to allow verification of credit and information.
Now they send me terms and card. There must be some execution of agreement. Usually this is designated by signature on the card and/or use of the card implying your consent and agreement to the stated terms.
If they send me a card with terms, this seems to me to be an OFFER of credit extended and I must accept it. I'm not saying that they don't report it even if I decline, I am saying I think there is a legal basis to seek its removal under consumer and credit laws.