This has happened many times to me.
Well I'm sure many others have the same problem.
It is not a perfect system, being green doesn't mean I am stuck to the front of the monitor, there could be a kaleidescope of reasons for missing a game invite.
For me, I have several computers, one of which is constantly hooked up to WGT and is set up for gaming. Other computers have different purposes, and whilst I may be green , it is quite possible I am doing something else on another computer
yes, I am lazy, and can't be arsed to switch red ( busy ) every time I leave my chair.
I too get frustrated at inviting someone for a game and having to wait 3 minutes for the default decline, it makes u wanna scream, especially when trying to set up a game with a stranger in a matchplay tournament..