I wouldn't call the interview process at Google broken. While some of my coworkers are better than others, I've yet to encounter any that truly aren't at the top of our field. Whatever we're doing, however we may fail in other areas, the primary goal of interviewing--to find and hire highly qualified people--is something we're achieving.

Yes, we may be rejecting highly qualified people who would do well at Google, but interview poorly. As has been noted in the comments here and elsewhere[0] it's far better to reject a qualified candidate than accept an unqualified candidate. Though we'd all be happier with a higher true positive rate, we're not willing to accept a higher false positive rate to achieve that.

What we're not good at, and what we get lampooned for so frequently (e.g., this story) is that in our pursuit of minimizing our false positive rate, we come off as arrogant, sometimes condescending, and a number of procedural and legal problems exacerbate that appearance. I've interviewed people that were right on the threshold between "hire" and "no hire", and like Joel advises, I wrote down "no hire". I'd love to tell these people what would have swung my opinion and ask them apply again in a year, but I just can't: it's too dangerous.

As far as interactions with recruiters goes, I can't really speak to those issues, since my experience in the hiring process was atypical (though not at all distinct in the ways we've discussed here so far, e.g. being hired for a company and finding a position after an offer has been extended).

Now, to answer your question, I have never interviewed anyone for a specific position. Every single person I've interviewed has been for engineering as a whole. People get interviewed for specific job ladders (e.g. SWE, SRE, SET, etc.) but the specific teams/projects a person will work on is decided after they've accepted an offer, as I understand it (and experience it myself).

[0] http://www.joelonsoftware.com/articles/fog0000000073.html