almostfamous,
Visiting campus, either Tuck or HBS, has no relevance to your admission. It's the information that you gather and feelings you develop about a school during your campus visit which makes all the difference. If you did not visit Tuck but demonstrated in your essays that you understand Tuck's culture and you have strong "fit" there, then it will reflect positively on your application. On the other hand, if you visited campus but could not draw any anecdote from your visit about your potential "fit" there, then it will harm your chances of admission much more.
Why does a school emphasize on a particular aspect needs some understanding. But again, this is just my frame of reference and people have different inferences. Hope this helps!
BTW...YSOM likes quirks. I read on a current student's blog. From what I understand good grades, good GMAT, strong ECs, outstanding WE won't be enough to get into YSOM. They admit people who think totally "out-of-the-box"!
PS: I am not a current student.