The “hands-off” press was mostly an early to mid-20th century phenomenon.
In 1884, in contrast, the biggest personal issue in the presidential campaign was how Grover Cleveland had fathered a child out of wedlock. Interestingly, he survived the attack by doing something unusual: he told the truth and acknowledged it immediately. It took the wind out of the sails of the accusation.
As for FDR, the bigger coverup was his disability. The press really didn’t know anything about his affair, because he was very discreet about it.