Yes, we do, but it’s not absolutely important. As long as a reader doesn’t notice a mistake in grammar or punctuation, style is something they don’t see. Good grammar and punctuation, which takes forms in the various coded formal writing styles, is really only important in it’s absence. That is, when a reader stops and notices a problem with it. If you write with another style and we don’t notice when we read, it’s acceptable, although AP style is generally preferred in the interest of overall style harmony. That said, we might use different headline capitalization sometimes for purposeful or accidental reasons. If you use another style, though, please still use AP’s style of quotation.
Link: http://www.gatehousenewsroom.com/2016/08/25/ap-stylebook-punctuation-guidelines-quotation-marks/