This is how I learned false eyes when I was playing Go. A false eye is an eye where any of its surrounding stones can be placed in atari, and saving them would necessitate completely filling in the eye. This sounds the same as what is discussed on this page, but...
I saw this diagram in seki:
That's a seki though, the atari can be used as a ko threat if needed (ie for a huge ko that you can't afford to lose.) So it's not an eye.
Moreover, under Japanese rules there is no points in seki, even if your group has a true eye.