Earlier quoted context omitted.
Exactly--I didn't quite say it explicitly, but part of the problem was my naiveté about working for a large company after a career of mostly startups. (And my summary of the project may have been overly short. It was a week of full-time work, with a plan of making it an ongoing 20% project.)
I don't think this is a large company vs. startup thing. In most companies, large or small, you're hired to fill a particular job opening (that's described as part of the recruitment process) and usually interviewed by the group of people who you'd be working with. Does anyone know of any other companies that do this kind of random assignment the way Google does?
If they are afraid of leaking information about what projects they are up to based on their job openings, that's actually easy to solve - advertise heaps and heaps of openings for many, varied and niche skill sets. Of course, only some of these adverts are real openings, but no one but outside google will know which ones are real openings. Hence, your competition cannot sniff your job openings to see what you are working on. This simply costs fees in administration and you reject every fake advert application.