It's not like Google, for example, is looking to hire you if you don't have one of the couple-dozen college names they're into on your résumé. But if you get hired by a contracting company that posts you at Google to do a contracted task, you'll get to put that "Worked at Google" experience on the résumé and get a leg up.

Plus some people (falsely) assume that the environment will be great because the company has a great reputation. At the interface of the contractor level, that varies widely. I had to go to bat at my old office because I randomly showed up on the weekend and found out all the contractors were working in 85-degree heat in an office building; the building turned the A/C off on the weekend to save power, and nobody had thought to ask it be turned on when we moved a whole contracting team in to work weekends.