According to the policy fellowship website, they are providing students “the opportunity to spend the summer contributing to the public dialogue on these issues, and exploring future academic and professional interests.” They’re also providing the opportunity for orgs without money to get good interns.
As I said in my post, my read of this kind of thing (and it’s similar to, say, Microsoft funding PhD students to do their dissertations which are not related to Microsoft) has always been that they want their names on good work (it’s good PR!) and they see it as a potential to help people who might be good employees in the future. The uncharitable reading is exactly what GTP says, that they’re hoping we’ll all be Google shills for life.
I can only say that through my experience, Google never asked me for anything, never tried to sell me on anything, and has never asked me anything about my research or anything else in the six years since my fellowship. I obviously can’t tell you for sure what they might have been hoping for, but like I said, if they were trying to influence me it didn’t work.