Says "Local Only" but seems to work fine (FiOS related?)

If I hover the mouse over the networking icon in the system tray on Vista
computers on my FiOS network, it sometimes says "Local Only." Networking and
Sharing Center shows a red X between the router and the Internet. Restarting
usually shows them as properly connected to the Internet. Eventually, though
(usually about 30 minutes to hours later), it will lose that and revert to
Local Only.

Diangnose and Repair doesn't change anything. In fact, Windows usually
reports back, "Windows did not find any problems with your Internet
connection." Sometimes it says that TCP settings are incompatible. I let it
change them, but the Local Only problem is still there and a subsequent
Diagnose and Repair then always gives the same "Windows did not find any
problems..." report.

Some of those machines are laptops. I never have this problem when I bring
those laptops to other networks (office wired or Wi-Fi, airport Wi-Fi,
etc.). This seems to be limited to my home FiOS network.

Note that as far as I can tell from using the system, it does have Internet
access. Web browsing, e-mail, GoToMyPC, VPN, all seem to work fine. My main
concern is that this "Local Only" report is a symptom of something more
serious. If it's just a known bug in the Vista system to determine if it has
Internet access, I guess I could ignore it.

Is this a universal problem with FiOS? I see a lot of people seem to have
issues with the Actiontec router.

Should I care, given that I do seem to have Internet access (is this a
symptom of something more serious, or just a bug in Vista's network
analysis)?

Thanks for any insight or guidance,
Colin