If you create a website with wrongly attributed quotes Google will pick it up. And the more people complain and link to your website as incorrect the more popular it will get and eventually people just start making memes and sharing on all social networks and then the quotes becomes true in the eyes of the googlers.
> If enough people say that the quote is attributed to the wrong person then does it become fact like the redefinition of "literally"?
I think that's funny as a question, but has the wrong premise. There is no 'actual' meaning of words; they have meaning only by mass human consensus. (What is the actual meaning of 'flumbiliable'?) By contrast, there is an 'actual' first utterer of a quote, whether or not there is any consensus on his or her identity.
(I suppose that you could argue, though, that it is only mass observation of a quote that makes it a quote per se, rather than just something I said; if I mutter something under my breath, and it later occurs as a widely quoted line in a movie, then should it be attributed to me, to the screenwriter, or to the character who said it?)
