Yes, students are arrogant and push for grades quite a bit. But I saw zero evidence of systemic catering to them as a whole or to any specific sub-population. I imagine the Development Office (the folks who would cater to the ultra powerful) may get involved in extreme cases? But it would be a huge to-do among the faculty (tenured faculty at Harvard and most elite institutions are incredibly powerful) and I never heard of it happening.
As an undergrad, I pressed for grade changes twice and was denied, reasonably, both times. As a TA at Princeton I was often pressed for grade changes and all were denied.
What almost certainly happened in this person's case is that the Professors either a) weren't tenured and couldn't bother with student push-back given a sea of work and anxiety (or mistakenly thought student perceptions matter), or b) were tenured and didn't care to deal with student push-back.