It should be if it were spoken that way, otherwise it's not accurate. Of course, that could depend on the context of the quote. If you are just communicating the information given then, sure, correct for grammar and whatnot. If it's to communicate the personality and/or attitude of the person, then you quote verbatim as it was said. That's why the term "sic" exists for quoting people, you are acknowledging that it is known the quoted statement appears incorrect. Because that's the way it was stated.