Having some personal knowledge of two events in Berkeley (including the one referred to in the above video), the orders that effectively were "stand down" orders came from upon high. The first, from Admin at UC Berkeley, and the one above from BPD administration with some conflicting tales of city hall involvement.
At least in CA (and to a good extent, OR and WA as well), there is a serious political reluctance to intervene against protesters and rioters that are to the left side of the spectrum. In CA's case, it comes from a continued rush to coddle the criminal and the deviant, and disparage all that might raise a hand to question the increased taxes, red ink, and socialist legislation.

