This does not seem possible. This county contains Gainesville, which back then apparently was a somewhat small town (it's so weird to see Dade County casting like 26,000 votes). I have no reason to believe that, even in 1928, Gainesville was exceptionally different from the surrounding areas.
Which pretty much assures that the results are either mislisted or something seriously freaky happened in the area - the turnout looks normal, though.
The state totals match what the clerk of the House of Representatives has for the election.
In 1972 in Arizona, Pima and Yavapai counties had some sort of ballot misfunction that caused many ballots to be counted for both a major party candidate and Linda Jenness of the Socialist Workers Party. A court ordered that the ballots be counted for both. As a consequence, Jenness received 16% and 8% of the vote in Pima and Yavapai, respectively. 30,579 of her 30,945 Arizona votes are from those two counties. My guess is that something similar happened in Florida.