Incorrect Windows 7 "No Internet Access" notice

I think I figured this out. In the "Internet Options" control panel applet there's a "Lan Settings" dialog with a "Autodetect proxy settings" checkbox. Unchecking that seems to have helped things.

Update A much better explanation of what is going on can be seen here:
http://blog.superuser.com/2011/05/16/windows-7-network-awareness/