"I don't recall a lot about these votes but they were not directly for Kennedy or any other candidate, but the media have always placed them in the Kennedy national vote total so as to give Kennedy more votes nationally than Nixon."
That was only in Alabama, where several of the Democrat electors were "free Democrats" (or some such term) who had not pledged to vote for Kennedy and went on to vote for Sen. Harry Byrd. In Mississippi and Louisiana, the there were three main slates of electors: Republicans, Democrats and "Unpledged Democratic Electors." People who voted for the Unpledged Electors have their votes recorded as such on every source I have seen, and in fact the Unpledged slate in Mississippi received more votes than either the Kennedy or Nixon slates and thus the Unpledged slate was elected as the electors from MS (they, too, voted for Byrd).
It is uncertain whether Nixon would have received more votes than Kennedy nationwide had Alabama listed a slate of "Unpledged Democratic Electors" like MS and LA did. However, had that happended, Nixon would have probably carried Alabama, although it wouldn't be enough to keep Kennedy below the required 269 electoral votes (back then) for victory.