Streisand was 22 in 1964 when her career kicked-off with Funny Girl. I think she (like Marvin Hamlisch) was more popular with the 'Silent Generation' (1928-45).
Alternate/additional explanation for the findings: cheating continued after the campaign, but wealthier students were less afraid of the consequences than poor students.
Alternate alternate explanation: wealthier students also stopped cheating, but corruption became even more rampant in the grading stage. A lot of papers were "marked" so that they could be recognized by the graders and given a more favorable grading.
I know people which were a constant 5 at math through high school but which got 9.85 in the exam (1-10 grades at the time).
Teachers preferred corruption to happen in the exam room, since it was the students cheating, than in the grading stage where they were liable.