I believe average GPAs are much lower at Berkeley and UCLA than they are at ivies though, is that correct?

Yes when I went there but dependent on whether it was graduate or undergraduate and department. Undergraduate lower division CS classes were graded assuming a normal distribution (standard deviations from average). In my opinion, it was mostly used as a weeding out process. Graduate classes had much higher grades, mostly As, some A-s... few B+s. I heard that undergraduate Chemical Engineering had especially hard grading. It was supposedly hard to maintain a B average in that major and that major had students coming in with much higher average SAT scores and GPAs.

That's correct.