Open Education does not require the Open Web, but they both share the principles and practices of an openly networked community (see connectedlearning.tv and hivechicago.org). However, Open Education practices are greatly amplified and scaled by the power and reach of an Open Web!
I doubt Open Ed requires the Open Web--wasn't one of the big impacts of the printing press to "open" education to the masses, so books weren't things that only privileged people could own and access? Andrew Carnegie and other proponents of public libraries could also be said to have been champions of open education in their time, in that they were trying to make education as freely accessible as possible given the constraints of technology.
At the heart of the issue both share a fundamental belief that knowledge belongs to all. Open Web believes the tools to encode and decode the path tothis knowledge should be transparent and available to all. Open ed then believes these paths should be available and transparent to all.