Rainman was actually Tom Cruise's character, the 'normal' guy, not Dustin Hoffman's autistic. (Yes, that bugs me when everyone and their mother get that backwards ;) )
A network always shares branding banners, company's announcements, polls, calendars… common information which goes often in sidebars, while the content belongs to the unique site.
No. Not a NETWORK. At least not in WP terms. You're confusing terminology that is, to be fair, confusing enough as is ;)
A network means "A network of WordPress blogs, all of which run off of one WP install, creating the MultiSite Network."
You're thinking like Sharepoint Networks (i.e. all sites under the umbrella). Nothing wrong with that, but that isn't how it works. And honestly, that's a situation where I would stop to think if I need separate full-blown sites or not. You do need to stop thinking about those terms in a locked way that 'Network == shared content' because that's not how WE use the term here :) Savvy?
If you need sites to share content like 'about pages' then I would hard code it into the theme so they can't remove the link, and have it all link back to the parent site. Or use a network-wide footer/header ( http://wpmututorials.com had a tute on that one). But you want to take the ability to change things away from the sites if that's your desire, because if they can change it, they will, and you'll spend more and more time wasted trying to lock MultiSite down, making it do what it's not intended to do, than actually using the product.
Look into Custom Post-Types, or categories, or the possibility that maybe not every site needs to be a cookie-cutter :)