Google hires into a general pool by design. It's because in companies where individual managers have hiring authority, every manager has an incentive to drop the hiring bar because it means he'll have more direct reports and more resources to accomplish his own goals. Perfect recipe for empire building.
The time to negotiate teams is after you get an offer. If you have any sort of negotiating leverage at all, you can probably exert some influence there. Basically, multiple managers "bid" on Nooglers, and then the manager from the highest-priority focus area gets him, modulo some input from the prospective employee himself. When I was hired, I was told I'd be working on Google Search, but the recruiter also said that if I didn't like that there were multiple managers in GMail and Apps that also wanted me, and I could go there.
In general, your goal should be to avoid getting marginalized. Typically, the highest-priority projects go to the best managers, who try to surround themselves with the best engineers, so your experience will be noticeably better on a high-priority project than a low one. The disgruntled Xooglers I know typically left because they got assigned to somebody's pet infrastructure project who somehow got headcount for a team of 3 or 4 but then has no idea how to run a software development project successfully, and no support for their ideas outside of their team. The happiest Googlers tend to be people in core Search, Ads, infrastructure (eg. MapReduce/Bigtable teams), research, or Chrome. These departments tend to feature large groups of loosely-knit, largely self-organized teams, and very hands-off management.
It could actually be a good thing that you ended up getting reassigned; it usually means that someone from a higher-priority area noticed your resume and swooped in with a bid. But you should be able to talk to the new prospective manager, or at least someone on his team. Every good manager I know will be happy to talk to a prospective Noogler that they want on their team if it means the difference between having them accept the offer or not.
BTW, I've noticed an interesting pattern where the culture of a focus area depends a lot on the first employer of the founder/SVP for that focus area. Search culture is Stanford culture. Chrome (which started from a bunch of ex-Firefox people) has a very open-source culture. Android culture is Apple culture with some Googliness thrown in (Android founder/SVP Andy Rubin worked at Apple for his first job). Google+ culture bears an unfortunate resemblance to Microsoft (Social SVP Vic Gundotra previously was in charge of .NET for Microsoft). Apps culture is a hodgepodge from various other companies (most apps were acquisitions). Infrastructure culture bears a strong resemblance to Bell Labs culture (former infrastructure SVP Bill Coughran was a VP at Bell Labs). I suppose the resemblance makes a lot of sense, and I wonder if other large companies have a similar effect.
For sure. Big industry names don't assimilate; they mold their environment to what they know (and they usually bring other people with them who come from the same place). Because of their clout, few will dare to disagree with them.
It is amazing how quickly a company's ecosystem can change when you bring in a big name from a different environment.