You do not need written authorization, but you do need a legitimate business need. If the applicant is truly prequalifying, you have a need. The loan officer should document the discussion and retain. I'm sure they are discussing the pulling of the credit report in the process of getting the person's SSN.
If the LO won't proceed because of the credit report info, they do trigger a denial (of course, you knew that, but do your LO's).