I was contacted by a Google recruiter once when I was a "programmer/analyst" but not for a software engineer position. I got as far as talking on the phone with the hiring manager, but was not called for an interview. Apparently I was obviously "not their type", but it wasn't a technical screen, so I don't think I was disqualified for lack of knowledge of say, data structures.

So, I still kind of wonder what it takes to be hired for a job that isn't the stereotypical Google SWE, because even though I didn't (and still don't) think of myself as a super genius, it's a fact that I was doing data processing for them which they were paying a handsome amount for (which didn't trickle down to me) so I felt I was qualified by definition.