I know kids who definitely got in because of parents money, but it certainly did not impact their grading.
What grade inflation really means is that for many, if not all, majors at a school like Harvard, you can take a path of classes that will end up with you completing your major and having a high GPA.
That said, there are certainly classes that will be much less nice to you when grading and have a self-selected group of students. My guess is that if JS has enough people from, say, Harvard, they will know the difference between a student who took hard upper level courses to complete their major vs. just the simple basics.
In terms of why this grade inflation is so prevalent, one reason I think is that faculty want to have students in their courses/run a "superstar" course, and students select classes with the easiest grading policy. Schools like MIT (and Princeton as well) specifically combat this and so are known for grade deflation.
I'll let others decide on whether they find that reasoning convincing!