Reason: In 1965, the girl received antibiotic penicillin and recovered. But the same thing did not occur with the girl in 1965 because they use the same penicillin. The reason the antibiotic doesn't work is because the bacteria strains "straphylococcus" evolve and grow resistant to the antibiotic. In 1965, the antibiotic selected against certain strain and those that survive the penicillin adapt and evolve due to mutation that help them grew resistant to the penicillin. In order for the girl in the story to survive, the doctor must NOT USE THE SAME penicillin and must create a new dosage that is more effective to kill the evolved strain of bacteria then she would recover.
This is the same reason why doctor must create a new vaccine for the influenza virus every single year because the influenza strain evolve really quickly and are able to grew and resist the antibiotic. Must of their resistant is due to mutation that allow them to adapt and resist the vaccine. (same with the problem above).