Vanderbilt is a pretty much completely open campus, and Fraternity Row even more so, all literally within sight of (and a longish walk from) downtown Nashville. Lots and lots of people who have nothing at all to do with Vanderbilt travel through and/or hang out in the Fraternity Row area all the time. Hell, for a long time, I drove through the campus on a regular basis just as a part of my commute.
Any idiot could have wandered into that area pretty much completely undetected and done pretty much anything.
About ten blocks from the Vandy campus is one of the three "big" synagogues in Nashville, and they have had anti-Semitic graffiti and the like there from time to time, as well. I've lived here for almost all of my 43 years, and I remember exactly one time when someone engaging in this sort of abhorrent behavior was a "local," either a student or someone who lives in the immediate area. IIRC, the last time that swastikas turned up at the synagogue, the responsible party was ultimately found to have been some couple from L.A. or Seattle or something like that.
It MIGHT have been some dumbass rich white kid living at a frat house along Vanderbilt Place or Carmichael or somewhere like that, and if it was, it was almost certainly someone who was too damned stupid to recognize that his "prank" was far, FAR more hurtful than he really realized, and such a person doesn't have nearly the hate in his heart that true neo-Nazi believers (or Klan members, or whatever) have. My money, though, is on some outside dickhead who is such a coward that he had to carefully plan some time to come along and engage in some petty, pitiful act of vandalism in an effort to strike fear into the hearts of people that he himself is too scared to confront face-to-face.