FWIW: I have interviewed twice at Google for Dir. Eng. jobs, both times going the distance. (Once rejected after a few weeks, once received an offer two months later, too late to accept.) In those interviews, I was never asked a seriously hard technical question, let alone an annoyingly academic and trivial one such as those in this post. Rather, I felt like they did a pretty solid job of understanding how I would engage with the organization and perform in the role.
Though the lack of technical rigor was not surprising in evaluating me for a administrative & support position, the lack thereof in the onsite portion was something I sent explicit feedback about afterwards.