They do, in fact, have to give a reason by citing the section of law under which the visa is being denied (e.g., 214(b) of the INA). This does not nean, however, that citing the law section is something that the applicant will understand is the reason for denial, or understand what the section of the law even means, or -- even more likely in the case of 214(b) -- agree with. So, from a practical standpoint, people don't believe they were give a credible reason for the denial.