It's hard for me, as a nerd, to admit, but the technology isn't really as important as my peers might think. As a customer service rep, however, I can tell you definitively that comfort with Internet use and culture is absolutely required for any kind of leadership these days. It has to do with staying in touch with your community and constituency.
This is exactly why I go on my rants that paying attention to your community is everyone's job. It's not something that can be delegated. If you don't know your customer how can you even begin to make important decisions about/with them?