The two biggest issues were (a) not understanding that a DPhil qualifies as "Master's degree or better", and not bothering to ask what it was; and (b) changing which job I was applying for three times without asking me.
When I turned up in Mt. View for my interview, I was greeted with "so, you're interested in a job doing X", to which the only response I could provide was "... I am?" My first interviewer did a heroic job of rearranging my interview schedule to make it more appropriate, but obviously there's a limit to how much you can fix on the interview day itself.
I don't think it's incompetence per se. They just interview people all the time and try to apply the usual Google techniques of scaling (which involve acceptable failure rates). Recruiters are sometimes staff and sometimes not.
A good engineer would have caught the problem right away, but apart from your phone screen, no good engineer looked at your resume until maybe five minutes before you were in the building. This isn't carelessness as much as mental self-protection. People are super busy there and they still do a lot of interviewing.
The system works best if you are a generic Stanford grad with no fixed ideas about what you wanted to be doing. If you are even a little bit unusual the gears can suddenly seize up.