The best networking I did in grad school was attending startup-related events. That got me my first paid gig, which led to greater street cred as a developer. Attending events held by the career center was a close second, because those led to interviews. Everything else was fluff.
I know that my PhD completely changes the nature of jobs I can hope to get - not really because of what I learned directly at my PhD, but for everything else.
Sure the majority amount of my/our time is spend sitting and working in the lab, but going to a few conferences per year, doing an internship most summers, and having weekly meetings with other researchers adds up to establishing a lot of contacts in the research community that I wouldn't have without graduate school.