It depends of how are counted Alabama's votes, since it has both a mixed Democratic slate of unpledged and Kennedy voters and votes being elector by elector.And mainstream historical accounts say there was no reversal in 1960.
Varying methods have been used to break down the vote into Kennedy and unpledged votes. One method is to take the 318,303 votes as Kennedy votes and the 324,050 votes as unpledged votes, giving a total much higher than the actual votes cast. Another is to take the 318,303 votes as Kennedy votes and the remainder (5,747 votes) as unpledged votes. A third is to split the 324,050 in the proportion of 5⁄11 to 6⁄11, following the proportion of electors, giving 147,295 votes for Kennedy and 176,755 for unpledged electors. In all cases, Republican candidate Richard Nixon of California, then Vice President of the United States, has 237,981 votes. If the last method is used, it means that Nixon won the popular vote in Alabama; it also means that he won the popular vote nationally. Congressional Quarterly calculated the popular vote in this manner at the time of the 1960 election.