No, it wasn't. In fact, at U of Wisc. - Madison, the old IDs had SS#s and then they were sued by students for being required to give that sort of info publically, so they went to a system of numbers.
When I did my TA work, the prof. wanted to have an ability to catch final exam ringers/id them by having the fathers first name on the exam (must fill in the blank or won't be graded)... when gradeing, we realized that being required to put a student id number (which could have been a SS# in teh old days) and a few collected questions like "mother's maiden name", etc combined with an address from a campus directory would almost be enough to issue credit cards.