Currently in 2011, the various browser vendors cannot agree on how to define offline. Some browsers have a Work Offline feature, which they consider separate to a lack of network access, which again is different to internet access. The whole thing is a mess. Some browser vendors update the navigator.onLine flag when actual network access is lost, others don't.
From the spec:
Returns false if the user agent is definitely offline (disconnected from the network). Returns true if the user agent might be online.
The events online and offline are fired when the value of this attribute changes.
The navigator.onLine attribute must return false if the user agent will not contact the network when the user follows links or when a script requests a remote page (or knows that such an attempt would fail), and must return true otherwise.
Finally, the spec notes:
This attribute is inherently unreliable. A computer can be connected to a network without having Internet access.