Auf der Uni, to me, sounds quite wrong =} ... if someone told me they were "auf der Uni" I'd assume they're on top of the building. https://books.google.com/ngrams/graph?content=auf+der+Uni%2C+an+der+Uni%2C+in+der+Uni&year_start=1800&year_end=2008&corpus=20&smoothing=3&share=&direct_url=t1%3B%2Cauf%20der%20Uni%3B%2Cc0%3B.t1%3B%2Can%20der%20Uni%3B%2Cc0%3B.t1%3B%2Cin%20der%20Uni%3B%2Cc0#t1%3B%2Cauf%20der%20Uni%3B%2Cc0%3B.t1%3B%2Can%20der%20Uni%3B%2Cc0%3B.t1%3B%2Cin%20der%20Uni%3B%2Cc0

First of all, grammar is not always logic, as it is a system which is constantly growing and evolving with times and the usage of speakers. 'an' respectively 'auf' der Uni are both correct, but used regionally different. For example: Ich studiere an/auf der Uni.

Yes it is logical! That rule exists for for objects liike tables, chairs, books, pictures etc etc (even people if the *exact* position they are in is critical (eg Ich stehe auf dem Tisch). However, when you talk about places - restaurants, universities, banks etc you need different pronouns. "an" is used with universities. The difference in german is actually the same as in English - I'm at the university, ich bin an der Uni are correct. I'm on the uni and Ich bin auf der Uni are not correct - and both mean that you are standing literally on top of the uni - which I presume is not what you mean!