DownIn3Green,
not quite right what you said, at least fot the B777-300.
If you have a tail strike without the "Tail Strike" on the EICAS, you can continue to destination (according to Boeing Bulletin).
If you get the message, yes, land at nearest suitable airport.
For the B777-200 is different because you don't have a tail skid.In this case, in both scenarios Boeing recomends to Land at the neares suitable airport.
Cheers