Anytime anyone asks you for your SSN, inquire as to why and for what purpose. Read the fine print carefully.
If they press you for it, and they are short on details, ask them point blank whether they intend to pull your credit. If they in any way evasive, assume the worst. Be persistent in asking whether they intend to pull your credit.
If you wanna be obstinate, and I would, I would tell them I don't see anything obvious in this form that they intend to pull my credit. I would go on to say that if they do pull my credit without my express permission and without expressly telling me when I expressly ask whether they intend to pull my credit, then they are violating the permissible purpose provisions of the FCRA, and they are subject to a fine plus my legal fees, and my attorney ain't cheap.