I honestly have no idea what ordinary people intend when they use quotation marks.
Quotation marks can be used to mark quotations, obviously. They can be used as scare quotes, to mark words or phrases which have implicature that you’d like to cancel. They can be used to mark titles of articles. Philosophers use them to highlight the use/mention distinction.1
But take this bit of administrative verbiage, which might be read as a reference to the Spike Lee movie if it weren’t for the lower-case:
This document serves as a guide to the expectations and standards of behavior and provides basic principles to assist the University Community to always “do the right thing.”