Typesetting is actually correct. In the days of the printing press, it was not feasible to have type blocks for single punctuation marks. The blocks would be too small and fragile. Punctuation marks were appended to the end of the letter. Instead of having a single block with a period (.) they had a block for each letter of the alphabet with a period. (a.), (b.), etc.
Making blocks for both (“,) and (,”) was an unnecessary expense, so they went with (,"), and the convention stuck.